Complex Numbers in Polar Form

[@TalhaKhan-1996]

Thank you sir Rob.. The thing that I won't be able to learn the whole semester you made me learn plus saved in my mind in 12.35 minutes video. Tomorrow afternoon is my calculus exam and tonight I'm watching you.. 😂. But Thank you so much sir. You earned a subscriber..

[@profrobbob]

Glad I could help...that's why I love to teach:) After you subscribe please share this free resource with your teacher and remind ALL your classmates to watch and subscribe too, regrow and everyone learns...BAM!!!

[@Kakashihatake-pk2cw]

Professor is still giving hearts after 9 years.

[@profrobbob]

Thanks for watching...I'm glad math never changes:)

[@edwarddjan8319]

Mmmm....

[@icecreamkhanewali]

Me: My handwriting is the best. *watches the video* My self esteem: Mr. Stark I don't feel so good.

[@profrobbob]

LOL...I liked this comment as well!!! You made my day! What's the most important thing we learned today? Conversion of complex number to polar form❌ That the font I use in my computer can be used in real life too✅

[@icecreamkhanewali]

Thanks prof

[@profrobbob]

@@icecreamkhanewali :)

[@oluwolepeter3603]

LMAO... SO ACCURATE

[@profrobbob]

@@oluwolepeter3603 BAM!!!

[@Esmara3]

12 years after and this is still doing wonders Thanks sir ❤

[@profrobbob]

@@Esmara3 Thank you!!!

[@IllShivyou]

8 years later and this video is so helpful. I have a complex numbers test soon and this has helped me a lot! Liked and subbed.

[@profrobbob]

Thanks for watching and subbing...good thing math never goes out of style huh?! Go pass that test like BAM!!!...and after you do, please share this channel with the rest of your class and especially your teacher so ALL the math students know where to find free help:)

[@jesseniahernandez1087]

I'm blown away.... Only a few times have I understood math material so clearly. All the little side notes that you say make me form connections that are easy to see once I realize that they are there. Thank you.

[@profrobbob]

+Jessenia Hernandez you're welcome and thanks for taking the time to study and sub to my channel! Tell all your classmates to watch and do the same:D

[@kairu9373]

You're an interesting and full of passion professor. What my professor taught for 2 straight boring hours is covered by your lesson in just 12 minutes. Thank you so much good sir!

[@profrobbob]

You are too kind! I do love teaching and appreciate you choosing my videos to learn from🙂

[@PigmentBlanks05]

Math And Music Are The Two Things That I Can Confidently Say That , After Posting It ; People Comes back To It All The Time And There Is Always Someone Listening To It And Getting Help From It :D Really Loved Your Class Sir , Have Lovely Day!

[@profrobbob]

What a nice thought to share and thanks for being one of those people who tuned into the math portion:) We hope you will take the time to subscribe and share this free channel with everyone to help us keep growing and helping others...BAM!!!

[@mathprof7776]

Hey, am a Math Teacher myself but i really enjoy watching and learning new ways of teaching from you.

[@profrobbob]

Thanks for tuning in..it's always nice to know we are also being supported by fellow teachers! We all have our own way of explaining things and can always keep learning from each other:)

[@alecvalerie8749]

I needed this for precalc. Thank you sir Rob for the calligraphy and the math.

[@profrobbob]

You're welcome...thanks for tuning in! (and thank whoever taught you to write and read cursive:) Don't forget to sub and share thru social medias and with everyone else you know who is learning from home now...BAM!!!

[@georgesadler7830]

Professor RobBob , this is another exceptional lecture on the introduction to Complex Numbers in Polar Form. Complex Numbers exist everywhere in Science and Engineering. As a former Electrical Engineering student at the University of Maryland, College Park, in early 1990's, I used a lot of Complex Numbers in junior and senior level courses.

[@supercoolmy]

Man you are an awesome teacher the first one who ever replies to your doubts immediately ! (its not the same with other maths channels) Thats what we call dedication..:)

[@profrobbob]

THANK YOU Sohaib for noticing the extra effort we put into making this channel groW! I hope you will take every opportunity to spread the word about my channel thru social media, friends, classroom and your math department to help us continue to help others:D

[@Aya-wv3rt]

You sir are absolutely amazing. You're clear, enthusiastic and get straight to the point. We need more math teachers like you.

[@profrobbob]

Thanks for the compliment and for watching...please take the time to like, subscribe and share this free channel with everyone you know..BAM!!!

[@1mahn]

The tremendous variety in mathematical content that you offer, is what separates you from other users. You've never failed to provide answers to all the questions I've had; rare as they are, and for that I'm very thankful. Once I stop being a broke college student I'll contribute to your noble endeavor. =)

[@vishalmahi]

Hello I m from india and I m preparing for iit jee advance 2020 and I use to see ur vdo and love ur vdo too much because the way u explain its really enthralling

[@profrobbob]

Thanks you from Florida for choosing this channel to study with! Best of luck on your JEE exam...I hope you pass it like BAM!!! Please take the time to hit the LIKE button and SUBSCRIBE and share this channel with everyone you can to help us keep growing and helping students like you all over the world!

[@AC-rv2em]

Thank you so much sir. I was relatively fuzzy on converting to polar form, and on converting back to rectangular, and this was the most concise lesson I’ve got so far! Thanks again!

[@profrobbob]

You are very welcome...thanks for choosing us to study with! Please take the time to like, sub and share this channel with your class and teacher and thru social medias to help us keep growing and helping others...BAM!!!

[@indiraj8776]

Your handwriting is GORGEOUS oh my gosh (Also thank u for the helpful vid)

[@profrobbob]

You're welcome...thanks for watching! Please take the time to like, sub and share this channel with everyone and if you need a break from math I also have a few cursive videos...BAM!!!

[@nayminthurain3280]

This part of the lecture was missed in my class. Thank you professor, you're saving my exam.

[@profrobbob]

WHOOHOO! I hope your exam grade is/was an A!

[@AvinashEdits]

You’ve saved my pre calc Honors grade this year! Thank you so much

[@profrobbob]

I'd call that teamwork...you sought out help and I was there to provide it! You're welcome and please don't forget to sub and share this free help with everyone, specially your teachers...BAM!!!

[@profrobbob]

Another #math lesson Closed Captioned

[@LazyChristy]

I love your spirit! You really make maths fun. I've been suffering because I haven't studied maths for years and am now studying undergraduate mathematics, but your videos really cheer me up because they all make so much sense! Thank you!!! =)

[@moyukhdattaroy9677]

"I know, I know I'M AWESOME let's not make a big deal about it" No doubt sir.....we all know you are brilliant Amazingly taught...Thank you sir Respect you so much☺

[@profrobbob]

+Moyukh Datta Roy I do funny shirt Fridays at school and have managed to carry them over into my videos...lol Thanks for watching and for taking the time to send such a nice compliment...please take the time to like, sub and share this free educational channel with everyone you can:D

[@moyukhdattaroy9677]

Liked and subbed. I have used your channel to learn logarithms too. All my doubts were cleared. You teach very well. Thank you for making such a helpful channel for students like us😊

[@profrobbob]

+Moyukh Datta Roy you're welcome and THANK YOU for all that!

[@sargerpd]

Its beautiful that i can check in with your teachings everytime we go over the material in class, thank you!

[@profrobbob]

And it's nice to hear that you continue to support my channel and take the time to show your continued appreciation! Students like you are the reason I teach:)

[@profrobbob]

Thanks for the offer, but my wife says Oregon may be too cold for her Florida blood:) I'm in my 17th year teaching high school math & now this youtube venture has consumed all of my free time (my choice) but you need a masters to teach college and right now all our energy is going into growing this channel. Someday my dream is to have the viewers and subscribers that PatrickJMT does...you know they say "you're never too old to follow your dreams" Thanks for the great comment!

[@nicolecanete6780]

I just wish my math professor would teach like you and radiates the same energy as you. Thank you sir!

[@profrobbob]

You're welcome...thanks for choosing this channel to study with! Please take the time to like, sub and share this channel with your professor as an additional study resource for their students...BAM!!!

[@TheJProducti0ns]

Semester just started and I’m in Complex Analysis. I completely needed this as a refresher. Thank you

[@profrobbob]

You're welcome..glad I could help! Please help us keep growing and helping others by subbing and sharing this channel with everyone...parents, students and teachers too...BAM!!!

[@leonard1871]

His calligraphy skills are over 9000!

[@profrobbob]

BAM!!!....I like that score:)

[@profrobbob]

I always have to remind my students to check the mode of their calculators when working with Trig functions:) I'm glad you figured it out and thank you for watching!

[@profrobbob]

Pi/2 is equal to 1.57, so -.98 is less than -pi/2 radians or less than -90 degrees and a negative rotation is clockwise. If you rotate clockwise less than 1.57 radians you are in quadrant 4.

[@meropepe4226]

The AWESOMEST teacher everrrr. Really enjoyed it 👏🏻👏🏻👏🏻 The t-shirt really describes you

[@profrobbob]

+mero pepe BAM!!! Thanks for choosing my channel to study with and for taking the time to share your appreciation and send such a nice comment! Please like, sub and share this channel with everyone to help us keep growing:D

[@OriginLevel7]

Thank you for all of your videos! I have been watching quite a few of them for awhile now and these videos have helped me more than the many hours spent in my college trig class. You are a great teacher and I think it is so great of you to devote time to this and do such a great job. Please keep up the good work!

[@T2Footballers]

Have finals on this. Didn’t understand anything going on. This is a life saver

[@profrobbob]

Glad I could help and I hope your final went well!...if so please be sure to like, sub and share this free study resource with your teacher...BAM!!!

[@profrobbob]

Square roots can be simplified of you can find a perfect square in your root. 18 has a factor that is a perfect square...9. Sqrt(9*2) equals 3sqrt(2)

[@ZonaALG]

Best teacher and I really like the way you make your classes have some life, kinda like doing jokes with your hands, Thanks!!

[@profrobbob]

You're welcome and thank you for tuning in and the compliments! Don't forget to like, sub and share this free resource with your class and teacher so ALL the students at your school know where to find over 700 videos of free math help...BAM!!!

[@---capybara---]

Thank you so much for these videos you put out! I normally learn from lectures but the pandemic had other ideas...

[@profrobbob]

You're welcome...thanks for seeking youtube help and choosing this channel ! I hope you will take the time to sub and share this free resource with everyone you know who is doing the same...teachers included! ...also share any other helpful channels thru social medias as well, that's how we all grow and remain free...BAM!!!

[@DComplexAnalyzer]

Thabk u Prof...... In your explanation, you calculated the value of the argument as arctan (-3/2), i.e, you didn't neglect any negative sign of a and b and u now added 2π to make it positive..........but some other authors and sources do neglect any sign of a and b, something like arctan (3/2)..... Why the descrepancy prof😊

[@ee2be270]

Thank you for your videos. Watched a lot of them when I was taking the calculus sequence. Now i'm back to review complex numbers for my circuit analysis class. BAM!

[@profrobbob]

Thanks for returning...please take the time to sub and share this free educational channel with your classmates and teachers as an additional study tool :D

[@profrobbob]

You're welcome & thanks for the motivating comment...that's another reason why I continue to do these videos & my wife and I work so hard at growing my channel! Private tutoring help can be expensive, alot of great teachers are retiring, motivated teachers are getting harder to come by and places like KZbin are growing in popularity because of that much needed additional help! Teaching is still my passion after 18 years and this is a way to share that passion!!!...So spread the word for me:D

[@tsotangchabane2677]

Great lesson Prof...I enjoyed it thoroughly. Keep up the good work of motivating us, you really make complex numbers a walk in the park. God bless u!

[@profrobbob]

THANKS Tsotang...it's always nice to hear that kind of positive feedback and appreciation from my "students"!

[@octaviotastico]

Amé el video, sos lo mas! Me ayudaste muchisimo. Lo apercio mucho. Sos mi profesor favorito. 8:43 BAMM!! -- I loved the video, you're the best! You helped me so much, I apreciate that. Nou you're my favourite teacher.

[@profrobbob]

Gracias! Thanks for studying with Tarrou's Chalk Talk...I hope you continue to enjoy these videos and if so, please subscribe and share with others so everyone has the chance to learn from these free lessons.

[@kiannn]

Youre awesome!! My test is next week wednesday

[@profrobbob]

I hope you passed that test like BAM!!! ...and if you did please sub and share this channel with everyone!

[@kiannn]

@@profrobbob Gonna do that with our next unit👍🏼👍🏼

[@profrobbob]

@@kiannn keep watching and sharing and reminding others to SUBSCRIBE!

[@profrobbob]

If the point is in quadrant 2 do 180 - reference angle, quadrant 3 do 180 + reference angle:) Thanks for watching!

[@daisyLia89]

Watching this video 11yrs later Tommorow i have an exam Thanks it was so helpful

[@profrobbob]

A little late, but I hope you passed your exam!

[@bhavesh.adhikari]

i am lost in a problem where i cant remember these things. thanks professor. everything is being recalled now

[@profrobbob]

And Thanks for watching them!

[@MrSpander]

thank you sir, you should move in with my wife and I, when we finish through vector calculus you can go back home. by the way, my wife cooks great food. you are awesome, i cant believe you dont teach at university level. you are far beter than the docs who teach math at WOU, in oregon. thankyou for your help.

[@DjFinestWorldWide]

You must be the professor with the most beautiful handwriting ever

[@antoinepatino2566]

Thank you Professor, I understand this perfectl now, , thanks God that your lesson save my exam.

[@profrobbob]

You're welcome! Thanks for tuning in...please take the time to like, sub and share this channel thru social medias, with your friends, classmates and especially your teacher as an after school study reference...BAM!!!

[@simranupasna1641]

sir. your teaching was.... just awesome.... what I wanted to get... I got..... thankyou very much sir...

[@profrobbob]

You're very welcome Simran...please take the time to subscribe and share this free study resource with your class and teacher too:D

[@simranupasna1641]

ProfRobBob yup... sure sir

[@profrobbob]

thanks!

[@dsd5705]

beautiful hand writing

[@profrobbob]

thanks...I have a video for that too:)

[@floydthulaningobeni7647]

I like the way you present, you make math look easy. Thumbs up, keep up the good work

[@rufarotatira4096]

Thank you very much this was very helpful, all the way from South Africa.

[@profrobbob]

You're welcome all the way from Florida and thanks for tuning in! Don't forget to like, subscribe and share this free channel with everyone...BAM!!!

[@profrobbob]

Thank you for saying so...and THANKS for supporting by liking and subscribing too! Please be sure to share your experience and my channel info with others...because that's how I groW:)

[@profrobbob]

You're welcome and thanks for supporting by subscribing and liking!

[@bernardojose45]

I LOVED THE WAY YOU JUMPED. hahaha... Thank you very much, sir for this brilhant explanation.

[@profrobbob]

I do that in all my videos...keep watching, learning and sharing this channel! We appreciate your support...BAM!!!

[@josephkaolinhugo7620]

I did not expect that hop haha but it radiated some good vibes here.

[@profrobbob]

Be prepared they are in 99% of my videos...BAM!!! Thanks for watching...please like, sub and share this channel with everyone:D

[@junyiqiu5583]

You are so an awesome, teacher. I subscribed all your videos. I love your teaching style as well. Please keep posting. Love it.....

[@profrobbob]

THANK YOU for choosing Tarrou's Chalk Talk to learn from and subscribe to Junyi Qiu ...I'll keep posting and you keep watching and telling all your friends to do the same:D

[@ritikagarg777]

Wow your handwriting is superb sir

[@profrobbob]

THANKS...I have lessons on cursive too:)

[@marckivancamama5447]

thank you very much sir, my professor already discussed this a long time ago but now I remember, my high regards for your clear explanation! :D

[@profrobbob]

You're welcome Marck Ivan Camama and thanks for taking the time to refresh your memory and study...and choose my channel to watch and subscribe to!

[@ashleyhughes5374]

ProfRobBob breaks this down where I can understand it, the textbook is like another language sometimes.

[@profrobbob]

BREAK IT DOWN... daaa dada dat. :) I can feel that same way looking at math books sometimes too! Thank you for choosing my math lessons to learn from and your support.... BAM!

[@lydiabusisoncube5831]

your lesson is awesome sir..i really enjoyed it..best teacher ever.

[@profrobbob]

Thanks for watching and the compliments...please like, sub and share this free resource with everyone...BAM!!!

[@wildenthusiasm]

Professor kindly mention the principal argument I'm a little bit confused in these two O

[@boipelojoe]

I like your hand writing!

[@profrobbob]

Thanks for watching...I have a few cursive videos if you need a break from math too:)

[@camarotony]

This precalc book we have to use for my online class is gabage. It explains hardy anything. To be honest, everything I have learned for this class has been from ProfRobBob videos. I have an A in this class thanks to you for turning the language of trigonometry into something we can actually understand and learn. Its not so bad when you know what your doing haha. Thank you!!!!

[@profrobbob]

CONGRATS on that "A" and for taking the time to seek outside help and choosing my channel to like, sub and study with...and for taking the time to share such a nice compliment! Please share this channel in any way you can with everyone you can to help us keep growing and remain free for others who make the time and investment in their future like you...BAM!!!

[@camarotony]

+ProfRobBob a students grade is (mostly) a reflection of the teachers ability to teach and help a student learn. Since I have used your videos to learn this online class and not my own professor, I believe you get the credit so again, thank you and keep doin what you do!

[@profrobbob]

THANKS, I'll take it!!! Thanks again for taking the time to seek out additional help and for choosing my channel to learn with... keep up that awesome work ethic...BAM!!!

[@leenomar399]

I hope you’re always doing well

[@profrobbob]

Thanks for the well wishes and for watching!..please sub and share too!

[@Eng.al-anoodal-manaa]

really I understand more then our professor in my class thanks

[@profrobbob]

BAM!!! Thanks for watching and please sub and share when with your class and teacher too:D

[@uusbilaajo6052]

I thank u teacher Bob. and even congratulate to u for getting rid off the loopholes in mathemaric by us.

[@profrobbob]

Thanks for watching and learning!

[@profrobbob]

Yes, I'm sure it is a real notation if it is in your book...but I am not familiar with that one.

[@DragusCalliforous]

love this man. Saved millions of us during the early 2010s from our psycho professors. Not even an honorable mention from the president. You're best Mr Tarrou. Happy Holidays.

[@profrobbob]

OMGoodness...I just searched your channel name and found your first comment January 2014...viewers like you are why I keep trying to keep this channel going and growing. What are you doing these days.....where did all that Calculus lead you in life? I just don't have much free time now that I'm teaching IB but I hope to make a few new ones over christmas break! Thanks for checking in, the compliments and appreciation....we with you a happy, healthy and prosperous 2022 as well...BAM!!!

[@itsurboibrad9719]

Perfect refresher for polar and complex numbers! Thank you so much for the amazing explanation and demonstration! :)

[@profrobbob]

Happy I could help...please help us by liking, subbing and sharing this channel with everyone...BAM!!!

[@vijayalakshmiramakrishnan6066]

Sir I have a doubt. How did you get the value .98?

[@mrmaul558]

The absolute value symbols in the |z| definition are extraneous. sqrt(a^2 + b^2) is always going to be positive anyways, on account of a and b both being squared.

[@profrobbob]

I am just using notation consistent with Complex Polar Form.

[@احمدزللي]

Thank you Sir Rob, it was a helpful video I liked your way of presenting best wishes to you Prof.

[@profrobbob]

You are very welcome...thanks for watching and learning. Thanks for the good wishes and please subscribe and share this channel with everyone!

[@NatalyF17]

Hello. Just want to say thank u so so much!! You are amazing at what you do! Keep it up!

[@profrobbob]

You're welcome and thanks for watching!

[@profrobbob]

That is simple...because math is awesome!!!!

[@blazeslavkovski9817]

BAM!!! Im Mr Tarrou

[@profrobbob]

Sounds like you got it!!! Please be sure to share it too...BAM!!!

[@vintagescorpio49]

At 5:01, you said you needed the absolute value sign but because the radical was there from the begining, don't you only use the positve anwer? What's the need for the absolute value?

[@profrobbob]

+Ayush Mishra I am being redundant there and emphasizing that only the positive answer is acceptable.

[@vintagescorpio49]

oh, so the absolute value isn't required right?

[@profrobbob]

+Ayush Mishra Correct. Sorry I caused some confusion there.

[@ledzeppelin4892000]

8:43...love it.

[@profrobbob]

BAM!!!

[@informn4tion]

WHATEVER!

[@andersnelson6464]

OKAY!!

[@profrobbob]

Thank you for such a complimentary comment! Comments like yours is why I work so hard on the continued effort to build and grow my channel. You can repay me by sharing my channel with everyone you know...share it on Facebook, Twitter, with all your friends and classmates, post a printable postcard in the student tutor center at your college, and anyone else you can think of:D Thanks so much for the support and choosing my channel to learn from...now BAM!!!...go start spreading the word!

[@samwatson5752]

there is a symbol for radians, superscript c, but its rarely used

[@MisterHumanMan]

That transition was so smooth 😂

[@profrobbob]

BAM!!!

[@wigglesg5202]

Thanks!! your a great teacher, really easy to understand

[@profrobbob]

You're welcome...thanks for studying with us:) Please share this channel with your class and teacher too and remind them to like and sub!

[@rararebancos5803]

I love this vid. You explained it very well, Sir. Thank you for helping us!

[@profrobbob]

You're welcome and THANKS for studying and subbing and sharing your appreciation Mae! Please keep sharing this channel too:D

[@maryalc8635]

BAM! Go do your homework. LOL that cracks me up at the end of the videosxD like your videos so much, finally understand polar and rectangular form! Hope I do good at tomorrow's test...

[@profrobbob]

THANKS Mary Alc ...I hope you go into that class and pass that test like BAM!!!

[@denny8360]

8:43

[@profrobbob]

BAM!!!

[@umairirfan9328]

Awesome video and beautiful handwriting

[@profrobbob]

THANK YOU! Don't forget to like, sub and share this channel with everyone and if you need a break from math I have a couple of cursive videos too :)

[@amitha1135]

Thank you for your explanation sir

[@profrobbob]

You are welcome😄👨‍🏫. Thank you for choosing my video to learn from. Please help spread the word to all of your friends and teacher.

[@jasmindizon]

Good day sir...you give me a superb session today 💪💪💪

[@profrobbob]

Thanks for watching and I hope you are continuing to enjoy learning form us...if so, please like, subscribe and share this channel with EVERYONE!

[@PowerSlaveAlfons]

I should buy that shirt.

[@aadarshawagle8916]

This made me clear. Thank you professor.

[@profrobbob]

You're welcome...thanks for choosing this channel to study with! Please subscribe and share it with everyone...BAM!!!

[@addoonalle2763]

_he is fantastic teacher_

[@profrobbob]

THANKS!!!

[@Thekingis23]

Love from india sir.

[@profrobbob]

Right back to you from Florida! Don't forget to like, subscribe and share this channel with everyone...BAM!!!

[@PlantEats]

I don't think the abs value brackets were required around the square root symbol when calculating the modulus. at 4:49

[@profrobbob]

+Plant Eats Yeah, I got a little bit over zealous there:)

[@will2win1234]

tan^-1(-3/2) = -0.98 How??? I got it as -56.309

[@spawnterror]

It's radians. Multiply by pi/180.

[@anoniem012]

Liked in the first second because of the "BAM!!! Im Mr Tarrou". I hope I will understand it (if not I will not remove my like :D) EDIT: Yes I understand his explanation! But I was looking for z^3 things in my class they used euler to solve it I don't know why.. :D

[@profrobbob]

Thanks for the like and I hope you will continue to find this channel helpful!

[@aalzien722]

thanks for explaining this. im struggling so much with this and it just drives me crazy when i cant understand something.

[@profrobbob]

You're welcome and good job on NOT giving up until you got it figured out!!! Those skills will take you far in life...BAM!!! Don't forget to sub and share my channel and your experience with everyone to keep us growing and helping others:)

[@Davidamp]

I love the sound of the chalck hitting the board, BAM!

[@profrobbob]

+David amp thanks for watching and there's plenty more to watch!

[@Davidamp]

ProfRobBob I know!! Thanks for doing all this work!

[@profrobbob]

+David amp you're welcome and thanks for taking the time to invest in your future...BAM!!!

[@_Anna_Nass_]

5:38 for where the formula actually starts. Just dropping this as a study note for myself

[@profrobbob]

Thanks for watching and learning and subbing! Please continue to share this free resource with everyone...BAM!!!

[@vhiedkc859]

greetings from Tanzania asante sana mkuu

[@profrobbob]

THANKS again!...sorry it took me so long to reply.

[@coliver3017]

At 8:00, I am confused by how and why you got 5.3 from 2pi - .98. Why are you doing that step

[@profrobbob]

2pi is 2(3.14) or approximately 6.28, and 6.28 - .98 is 5.3. I am doing this because the point is in quadrant 4 and I need a standard position angle that has a positive measure in quadrant 4.