A-level Mathematics 9709: Argand diagrams and loci

[@ThomasCambridgeMaths]

Note to label the horizontal axis "Re(z)" and the vertical axis "Im(z)" (do as I say not as I do... missed it!)

[@Abrar_Alek5470]

Whew, this is probably the third time I've finished this p3 playlist. Gotta say, its been an honor to have been taught by such a genuinely caring and awesome teacher! Thank you so much for helping us like this Mr Thomas, really enjoyed the time I've spent here learning from you! Now its time to ace my exams and I pray to god for your success! Take care teacher🎆

[@ThomasCambridgeMaths]

Great to hear Abrar! What country are you in? Are you at a Cambridge school, or independent study? November 2022 series?

[@Abrar_Alek5470]

@@ThomasCambridgeMaths I'm in Bangladesh as of now! And yes, have given my exams privately this current series . Hoping my results are going to be good!

[@ThomasCambridgeMaths]

@@Abrar_Alek5470 Good luck! I taught in Mandalay Myanmar when I made those videos, now in the US, but one day I hope to teach A Levels again!

[@Abrar_Alek5470]

@@ThomasCambridgeMaths Thank you so much!! One thing I can confidently say is that you're an amazing teacher and you'll be saving a lot students whether its O,A-levels or Gcse! And yeah I've seen your introduction video and it is pretty cool to know that you've been teaching in a neighbouring country of mine! Stay well Mr.Thomas :))

[@AllanLovezGaming]

This is actually one of the best video I has seen. Thank you so much for taking your time out of your day to make this video for us :D

[@AllanLovezGaming]

It has really helped me for my last minute revision

[@ThomasCambridgeMaths]

Thank you MIcroO! If you're taking PM3 this month, good luck!

[@thefairylightstudio]

Thank u sir, U hv saved me from the torment of drawing Argand diagrams bcz I dint understand nothing. Thank u so much, God bless u immensely💖

[@ThomasCambridgeMaths]

Welcome Noor!

[@dussamcode]

perfect explanation. Thanks for summarizing the concept

[@ThomasCambridgeMaths]

Welcome dushsam!

[@Kishaarrrrrrr]

Thank you so much for this sir, this really helped a ton 👏🏿

[@ThomasCambridgeMaths]

Welcome Kishaar!

[@sethupathys641]

Thank you so much for explaining this!

[@ThomasCambridgeMaths]

Welcome seth!

[@siddharthdeshmukh7026]

Well explained thank you sir!

[@ThomasCambridgeMaths]

Welcome Siddharth!

[@spookhie5882]

Just gained yourself a new subscriber...thanks for the help

[@ThomasCambridgeMaths]

Welcome Spookhie!

[@sarfrazahmad2580]

does the initial horizontal line in the case of half-line always has to be towards the left side of the point.

[@ThomasCambridgeMaths]

Hi sarfraz, the broken reference line is at an angle of 0, which is the direction directly right from the starting point as diagrammed at 3:11; the actual half-line is drawn based on the angle as diagrammed at 3:15.

[@sarfrazahmad2580]

@@ThomasCambridgeMaths thank you.

[@saranaeem1859]

basically for drawing the perpendicular bisector do we have to like plot points with the equation

[@ThomasCambridgeMaths]

Hi Sara, these are sketches so you can draw in a perpendicular bisector without plotting points. If a question were to ask something like "what is the imaginary component of the locus when the real component is 3" then you would use coordinate geometry to find an accurate answer, but the drawing can be at "sketch" precision.

[@lin7556]

you saved me bro, best video ever. Thx a lot : )

[@ThomasCambridgeMaths]

Saving lives... it's a great day! Thx lin

[@MiniCuberr]

How about the third example if it was inequality? Thanks.

[@ThomasCambridgeMaths]

Hi La Moon, in this example shade left side if >= (all points closer to (1, -1)), shade right side if or < without =, use dotted line.

[@niammell9391]

majestically explained, thank you

[@ThomasCambridgeMaths]

Thank you Niam!

[@targetmurima1760]

But I have a question though... do we shade the wanted or the unwanted region...?

[@ThomasCambridgeMaths]

Hi Target, for shading-required workings, A Level usually you shade "wanted" region; IGCSE usually you shade "unwanted" region, so if you started with IGCSE and are now studying A Level, notice the difference... and of course be sure to follow the given requirements for a question.

[@targetmurima1760]

@@ThomasCambridgeMaths excellent... thank you Mr Thomas

[@kingmonk9981]

Uhm i dont get wwhen you were on the circles and said -4 but it was actually negative 3. was that a mistake?

[@ThomasCambridgeMaths]

Yes, now updated, you do use -3 for both y values - thanks!

[@priscilla_wong]

Thank you so much for the video. By the way, do we need to shade the circle to indicate which area is covered or just using dotted lines is sufficient? Thank you :)

[@ThomasCambridgeMaths]

Hi Priscilla! If the notation is

[@priscilla_wong]

@@ThomasCambridgeMaths Ok, thank you so much for the clarification Mr Thomas! 😁

[@targetmurima1760]

Great work. Thank you

[@Sarah-wh5ux]

what would you need to do if you had arg((z-2i)/(z-6)) = 1/2 pi

[@ThomasCambridgeMaths]

Follow the division algorithm at 1:30 in this video kzbin.info/www/bejne/jonPioCVmMuao5I to get real and imaginary parts you need, then the procedure is similar to the second example in this current video.

[@AlExAnDeRThEoDoRuS]

supercalifragilisticexpialidocious

[@ThomasCambridgeMaths]

Welcome zarif!

[@superdudeyang8705]

For the half-line (ray), I believe the origin of the half-line should be an open circle because the point itself has an undefined argument. If you substitute that point into the equation, you will get arg(0) = 4pi/3, which doesn't make sense. Just clearing something up haha.

[@ThomasCambridgeMaths]

Hi Superdude, correct - I am using the "loose" notation from Cambridge A Level; if you use your notation on 9709 PM3, include the first sentence of your justification above.

[@superdudeyang8705]

@@ThomasCambridgeMaths oh im from australia so maybe stuff is a bit different, good video nevertheless

[@perfectstranger1735]

Great explanation;but a question can we draw the perpendicular bisector with help of the compass?

[@ThomasCambridgeMaths]

Hi 173, for a drawing as a visual guide you can use tools; for examiner requirements, you need to show the calculations (described by Cambridge as "solutions by accurate drawing will not be accepted").

[@tinashechiduma5090]

You're a life saver 🙏🏾🙏🏾🙏🏾

[@ThomasCambridgeMaths]

Welcome Tinashe!

[@aliabbasdhalla8213]

I didnt understand the part of extensions

[@ThomasCambridgeMaths]

Hi Aliabbas, if you can give me a time range in the video I will review and get back to you, thanks!

[@danielngo6037]

Can you make a video to find max and min arg(z)

[@ThomasCambridgeMaths]

Geoff did it for us! kzbin.info/www/bejne/n6jUoYCQqZefmaM

[@danielngo6037]

@@ThomasCambridgeMaths ive also watched his video and just wondering how to find max and min of arg(z + constant). There was one question like that appear in our test where (0,0) is inside the circle and we cant find neither max nor min since it will be infinite. Question was [z-2-3i]=5, find max arg (z+12).

[@ThomasCambridgeMaths]

@@danielngo6037, is it a past paper question? Which paper/question number? Or is it a independent question?

[@danielngo6037]

@@ThomasCambridgeMaths its an independent question.

[@ThomasCambridgeMaths]

@@danielngo6037 is the answer 0.422 radians?

[@KhanhNguyen-kv1oh]

Thank you so much!

[@ThomasCambridgeMaths]

Welcome Khanh!

[@realmilk06]

240a84 x 234 = 56b90256 how do we solve this sir?

[@ThomasCambridgeMaths]

NiKkKOo, search for "olympiads alphabet number" for resources, good luck!

[@realmilk06]

No I can’t find it

[@ThomasCambridgeMaths]

@@realmilk06 The method (not the solution) is here: kzbin.info/www/bejne/a2SrdJSCac2badE

[@ThomasCambridgeMaths]

Follow the video, then attempt your example using the same technique.

[@realmilk06]

Ohh got it now

[@nethunranasinghe2539]

Thank you so much sir👍🥰😊.

[@ThomasCambridgeMaths]

Welcome Nethun! If you're taking the paper in the Oct/Nov series, let me know, I'm putting together a study group to work on past papers for PM3 and Mechanics. You can contact me at my PM3 webpage; www.quia.com/pages/thomasdavis/9709pm3 email link at the top.

[@nethunranasinghe2539]

@@ThomasCambridgeMaths Actually sir im from sri lanka.Yes im taking my A-Level examinations on 12 th of octomber,but im little bit confused😅. I dont think they are the same. I think the exam you mentioned was "Cambridge A-Level" s right? . Anyway sir you helped me a lot.This part was a headache for me.You explained it in a very simple way that all my problems and confusions were gone.Thank you ! 😊

[@azfarhasan5435]

7:50 Why are you pronouncing your L's like that. You pronounced them fine in the beginning

[@ThomasCambridgeMaths]

Hi Azfar, not sure but sometimes I create the videos in multiple sessions/splices, so the new L could be the result.

[@adderallclimax769]

THANKS BC I WAS SLEEPING DURINGMY MATH CLASS BUT YOU HELPED SO MUCHHH

[@ThomasCambridgeMaths]

Welcome adderall!

[@stephaniexx558]

thank you so much

[@ThomasCambridgeMaths]

Welcome Stephanie!

[@clement_jacob]

perfect vid

[@ThomasCambridgeMaths]

Thank you Clement!

[@rivoobagchi5245]

thanks so much!

[@ThomasCambridgeMaths]

Welcome Rivoo!

[@drftsofficial7016]

BRO THANKS MAN

[@ThomasCambridgeMaths]

Welcome drfts!

[@mayashomarieh7941]

Why did I just find your channel

[@ThomasCambridgeMaths]

Welcome Maya!

[@basedyapper]

Yayy thank youu

[@ThomasCambridgeMaths]

Welcome sage!

[@abdulmageedalshahrany1688]

legend

[@ThomasCambridgeMaths]

Thank you Abdulmageed and best to you!

[@leonidas7698]

@@ThomasCambridgeMaths tr. Thomas, i m Freddy from imso i want to know how many peoples can go to vietnam except for the scholars

[@ThomasCambridgeMaths]

@@leonidas7698 up to 20

[@jameschambers9177]

I gooned to this video, good math😫

[@ThomasCambridgeMaths]

Welcome jameschambers!

[@muhammadabdurrahim752]

Nice vid

[@ThomasCambridgeMaths]

Glad to help Muhammad - best of luck on A Levels!

[@nhartolojacky3344]

thanks

[@ThomasCambridgeMaths]

Welcome Nhartolo!

[@jordabox]

x1.5 >>>>

[@ThomasCambridgeMaths]

Welcome jordabox!

[@mayashomarieh7941]

Wow seriously

[@ThomasCambridgeMaths]

Yes seriously!

[@mayashomarieh7941]

@@ThomasCambridgeMaths Thank you so much

[@madansingh8070]

cool explanation

[@ThomasCambridgeMaths]

Thanks Madan!

[@jcn268]

baby question try explaining some harder versions of these topics

[@ThomasCambridgeMaths]

Hi Jin, the topic covered here is Cambridge International AS & A Level Mathematics 9709/Pure Mathematics 3/Topic 9 Complex numbers, represent complex numbers geometrically by means of an Argand diagram; for other topics I am sure KZbin has good content.

[@sanuratennakoon7979]

Thanks

[@ThomasCambridgeMaths]

Welcome sanura!