Rectangular to polar form of complex number | Precalculus | Khan Academy

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
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[@Alberpinypon]

This video is terrific. We all think that the basis are always clear, but without realising we end up doing calculations without thinking what everything means. Just a great way of explaining sir. Hands down.

[@frostbitepokin9520]

Alberto counterCOCKwise

[@jakobsime4190]

@@frostbitepokin9520 ?

[@DualWielded_]

cap

[@manindrademel5779]

I learnt more in the first two minutes of this video compared to the 1 hour and 40 minute class i had today

[@benjaminpan1073]

True

[@brayanmani7112]

You have 1 hour and 40 minutes of class 🤯🤯

[@neutrogemax8494]

@@brayanmani7112well yeah how long are your classes

[@brayanmani7112]

​@@neutrogemax8494Maximum 40 minutes bro. 😂

[@ethanniles8174]

“So I’m going to construct a unit circle here. So, construct a unit circle. So this right here is a unit circle, circle of radius one. So construct a... unit circle. That’s a unit circle.” Nice

[@Personal-jr9rn]

Yeah that is the only thing that bothers me from learning from him but still I can't find any one better than him

[@joranmulderij]

Most Khan Academy videos are pretty slow paced. I only tend to use them when I really get stuck on something. But in case I do really get stuck, Khan Academy almost always makes me understand it.

[@LittlePrincessatB-612]

This video has saved me from my teacher's slides. Thank you!

[@xgg4017]

i feel like in class its just taught to you as something just is the way it is, i rly appreciate these videos online that actually demonstrate the background explanation for why things are the way they are....like if something makes sense because of where it is derived from, then its like so much easier to remember thanks for the amazing vid :)

[@n0lain]

Countercockwise Joke's on me I'm about to fail this subject test

[@nickbeats9883]

Did you fail?

[@n0lain]

@@nickbeats9883 Nah pretty sure I got like an A or a B. Ended the class with like an A- so that's a dub

[@hudaismail6735]

@@n0lain that was 3years ago I don't think I'd have remembered at all

[@n0lain]

@@hudaismail6735 to be fair I 100% forgot about my comment, I came back cause of the notification

[@g.3rd]

@@n0lain Did you forget about this one too 3 years later?

[@criticalangle90]

This actually gives context to complex numbers. It actually makes sense to someone like me who hates imaginary numbers. THANK YOU!!!!!!!!

[@authenticwarrior7877]

superb teaching skills....

[@frostbitepokin9520]

authentic warrior counterCOCKwise

[@MrArthur2312]

7:40 the angle is actually from x axis right side to the complex argument clockwise thts why its pi+the angle

[@ridanoorani3525]

How do we go back to the (a+bi) form?

[@garrettremaley6737]

OMG thank you so much! You've quickly explained what my teacher couldn't explain in weeks.

[@frostbitepokin9520]

Garrett Remaley counterCOCKwise

[@sdeshpande09]

The explanation for deriving theta can be much simplified if r was calculated first,and then use the definition of tan theta to derive theta.

[@GtaRockt]

thank you so much. I never understood why the angle has so many different ways to calculate, considering if a or b are either positiv or negative. you are the man!

[@frostbitepokin9520]

Lobster with Mustard and Rice counterCOCKwise

[@Superegio42]

I stay up late to watch stuff like this.

[@EXHellfire]

so badass

[@frostbitepokin9520]

counterCOCKwise

[@ginaxs7975]

2:30am😭

[@InSterquiliniisInvenitur]

The reason for using r cis (θ) was not explained by my textbook in a way that made sense to me. This video helped a lot.

[@azizahputri632]

Wow the explanation is very clear, thank you so much sir, you really helped me!

[@stardust-reverie]

countercockwise

[@Permafrostrock]

Straight and clear explanation. I would have loved it before we first used the polar form in geophysics :D

[@emilycaballero6052]

"These are not the thetas you are looking for."

[@renatoh.santos5212]

I know hahahahahah

[@Jo_Es_Chess_Channel]

Respect. Only sexual joke that doesn't involve countercockwise

[@AShad95]

Hahaha "counter cockwise" at 11:50. Great video though, very helpful

[@theartemys]

Yeahh XD

[@Personal-jr9rn]

omg i don't understand where is the issue

[@westeast6229]

Im an Algerian student who is in his last year of high school and unfortunately this is in our program, you are actually a god send my friend

[@jordanbonner8405]

This finally lit the light bulb. Thank you

[@erd44]

Thank you, it was very helpful. For me, finding theta would have registered better in degrees, idk if anyone else feels that way.

[@pnkmimi1323]

thank u for actually explaining it properly

[@fikrattalibli2433]

The whole complex numbers in 12 minutes!

[@milesemanuelpaavola7994]

Thank you again, your videos can be a Godsend at times. :-)

[@mohanadabdulrahim7202]

2020 and still learning from him

[@chngkai2744]

it is 2021 now

[@martinuusss]

I learnt polar coördinates in the form of (r, Phi) (Phi = your Theta, guess that's not universal) which IMO makes it even clearer, you go 'r' away from (0,0) with an angle of Phi. Example: (r, phi) = (2, Pi) -> Z = -2 (+ 0i). (r, phi) = (sqrt 2, 1/4 Pi) -> Z = 1 + 1i . Thanks for your video, and I must admit, 720p + a new mic makes for a much better experience than your older complex number video's from 2008 ;-)

[@WSTSWISS]

this was soo good! thanks

[@govindnair3135]

Sir , you could have used triangle of vector addition,and resolution of r into 2 components.

[@RedBar3D]

The part at 3:50 wasn't all that obvious to me. What made me "accept" the statement was thinking of the two triangles formed; they're uniform. And since the hypotenuse of the smaller one is 1, the x- and y-coordinates must be r*cos(theta) and r*sin(theta) respectively. The books I've had and have tend to show that this holds for right angle triangles (they don't even mention the unit circle) in the first quadrant, and then state that it holds for all quadrants (ie. not actually proving it). I'm not sure whether it's me or the books, I refuse to accept things without solid proof. Thank you for the video :)

[@user-hd2xe1ds1n]

Its because of similar triangles If triangles have equal angles they are similar and that means that ratio of sides are equal

[@billtruttschel]

Some trig books would abbreviate the last part as sqrt(13)CIS(2.55).

[@PimpMatt0]

Liberal arts have taken over the term CIS for Cisgender.

[@code5829]

They added new function “trans” to coexist with CIS

[@machinegunnasty1124]

Does he have a video on Polar to Cartesian?

[@Optimistic30021]

I was lost at -0.59 + pi. Why wasn't the calculator correct? Something about needing to shift by adding pi, but that was confusing to me.

[@dalenassar9152]

THANKD MUCH FOR ALL OF THE LESSONS!!

[@code5829]

Working from the problem is key

[@neyazahmad362]

Amazing 😊😊

[@redwestanimation541]

since pi is 180 you're supposed to subtract not add

[@durgaipriyads7205]

GGGGGGreat explanation sir

[@em1494]

Question: how would you find the modulus argument form of JUST a real number or JUST an imaginary number (ie: -20 or 3i)? My textbook has questions like these but I have no idea how to go about solving it?? I thought I was good at maths lmao

[@Klikmac]

well the argument of just a real number would be zero and the argument of just a complex number would be 1/2pi as they're just sitting on their axis

[@furqaanilahi8078]

@@Klikmac my question is since the real number is negative, then it is on the -ve part of real axis, is the angle pi??

[@klc032287]

Like the new mic.

[@samuelkoomson5369]

Very helpful.

[@AlessandroZir]

thank you! very useful and clear;

[@yashesvii]

Thank you!

[@jibby1274]

how did you know to add pi to theta

[@hamburgeor6567]

I love you Sal Khan

[@Raphael-ql9pf]

7:50 my own learning checkpoint

[@mch86]

thanks but I GOT ISSUES ON TRIGONOMETRICS AS WELL I WILL SURELY WATCH IT AGAIN AFTER A TRIG REVIEW

[@Mastermism]

This has been very helpful, thanks.

[@sarimansari9701]

Well.. In terms of understanding... I lost it from 2:06.... But I can surely say that whatever happened after that IS really interesting... ✌

[@emilycaballero6052]

Thank you for saving my life

[@arundathivarma7209]

this was very helpful...thank you :)

[@budahbugahbugah6573]

Lol im so immature as soon as I heard counter cockwise I rushed to the comment section to make sure I wasn't just hearing things.

[@richardlighten7076]

excellent video , hugely helpful **

[@Darkreign1]

is it okay to do this in degrees or does it need to be done in radians?

[@suryavikramrizal3462]

thanks Sal...

[@markbossman5103]

SAL YOUR STILL THE MAN!

[@I-VisiBomb-I]

+Mark BossMan You're.

[@markbossman5103]

give me a break loser

[@I-VisiBomb-I]

+Mark BossMan says the guy that learns calculus but doesn't know simple grammar.

[@jacobm8242]

+I VisiBomb I This is a math lesson lol, not english.

[@I-VisiBomb-I]

Jacob Mikeska in which you use letters from the English language.

[@josephrichardson5561]

Is this the same when working out British numbers?

[@tahseenalaa7030]

thanks so much :)

[@stefanovetri6058]

Couldn't we use inverse sin or cosine to find theta??

[@michaelhawkins8095]

Hey, anyone.....at 3:41, Khan said that x is sin and y is cos. I thought that it was the other way around.

[@kaethis]

11:50

[@ginaxs7975]

Where does the e come into this? Like re^(i theta)?

[@nikonoy3564]

How did you get cos(theta) is it same as cos(pi - theta)

[@luisangelzeferinocuautle3306]

What program do you use?

[@seeuclon]

can we now figure out what r and theta R?

[@Tyler-kh6gp]

Ngl, I upvote all Khan Academy videos before watching them because I already know they're going to be good

[@AleLox]

Miguel Diaz

[@evanbyrne3192]

how come its cos teta is that not the tan quadrant?

[@mohammedhafizurrahman3761]

314k views and only 580 likes??

[@siddharths2443]

Cuz mostly people use the site,hence they view the embedded version of the video where they cannot like the video.

[@frostbitepokin9520]

counterCOCKwise

[@sasakoncar]

i(t) = 20·cos(18570·t − 2.8798) how to get rectangular of this?

[@boshboshish]

I don't know why did you put the angel in rad should it be tan -1(-2/3) = -33.6 degree right away ?!!

[@ghassan308]

No, Precalculus is part of Calculus and in calculus you use radians for the trig functions

[@frostbitepokin9520]

He did it because it’s counterCOCKwise

[@michaelhawkins8095]

And...stop laughing at his 11:50....very mature KZbin...very mature.

[@mrmathmonkey9582]

quick question can you do this questions in degrees without using any radians...?

[@TheCherryify]

Why can't you just get theta right away by doing theta = arctan2/3 then pie -arctan2/3 = 2.55?

[@n.t3026]

woah

[@comprehensiveboycomprehens8786]

Pause at 3.20. Think.

[@muhammadnafees7514]

sir which application on computer for lecture like as a white board?

[@compleks1997]

Honestly it looks like it's MS Paint

[@oneinabillion654]

Hi, is a complex number always relative to the origin

[@furqaanilahi8078]

I think yes, sorry a little late (4 yrs late 😂)

[@oneinabillion654]

@@furqaanilahi8078 is ok, it wasn't the right question 😉

[@sphinx19]

tan-1(-2/3)=-33.69 degree??/??

[@Assault17]

Change ur calculator to radians 😂

[@josephrichardson5561]

I don't get it try and do this question why is every e.g. Got - as the real number and not plus instead. Try z equals to 5 plus 2j.

[@scarleteyes415]

Why did 90% of people in the comment section not understand? I don’t get it, what is it that you don’t understand? I may help.

[@yousefhamdan3188]

It's 3 AM . Why I'm watching this

[@frostbitepokin9520]

Yousef Hamdan because counterCOCKwise

[@normal_person1]

I DIDN'T GET IT

[@abloodorange5233]

Why my teacher just doesn’t explain exactly what the question will ask like you did only God knows. Wasted a week of my life.

[@vidiptsomeshwar7414]

isn't this pretty much the same thing as vectors?

[@allenburt1475]

Just wait till roses and crap

[@Drderp-hd5bb]

wish u kept it in degrees

[@susannamenlamenla8283]

"

[@Tensho_C]

This comment section is immature af I love it

[@josephpanes3430]

i dont understand

[@JustANobody910]

This video didn't really help me much....I need more example problems

[@Hazit90]

I love you Sal. (no homo)

[@zubax91]

complete waste of time, should have just shown the last 5 minutes

[@rapgaming2122]

very pathetic .....be more clear

[@MattMelon519]

I have no idea what the hell you are talking about.

[@smoaf2010]

countercockwise