Problem With An Argument | Problem 378

preview_player
Показать описание
▶ Greetings, everyone! Welcome to @aplusbi 🧡🤩💗
This channel is dedicated to the fascinating realm of Complex Numbers. I trust you'll find the content I'm about to share quite enjoyable. My initial plan is to kick things off with informative lectures on Complex Numbers, followed by a diverse range of problem-solving videos.

🤩🤩🤩 A Very Interesting Exponential Formula: zᵃ⁺ᵇⁱ = c+di

When you purchase something from here, I will make a small percentage of commission that helps me continue making videos for you. ❤️ ❤️ ❤️
Recently updated to display "Books to Prepare for Math Olympiads" Check it out!!!

🤩 Don't forget to SUBSCRIBE, hit that NOTIFICATION bell and stay tuned for upcoming videos!!!

▶ The world of Complex Numbers is truly captivating, and I hope you share the same enthusiasm! Come along with me as we embark on this exploration of Complex Numbers. Feel free to share your thoughts on the channel and the videos at any time.
▶ MY CHANNELS
Future channels: TBD
▶ EQUIPMENT and SOFTWARE
Camera: none
Microphone: Blue Yeti USB Microphone
Device: iPad and apple pencil
Apps and Web Tools: Notability, Google Docs, Canva, Desmos
LINKS

#complexnumbers #aplusbi #jeeadvanced #jee #complexanalysis #complex #jeemains
via @YouTube @Apple @Desmos @GoogleDocs @canva @NotabilityApp @geogebra
Рекомендации по теме
Комментарии
Автор

I think the theory of linear algebra is interesting, but performing the techniques needed to find answers is a lot of work without being interesting.

iabervon
Автор

Always appeal to geometry if you can. If you subtract i from a point z, you lower z by 1 unit (-i). And when you do, you end up on the 45 deg. line (PI/4). Therefore, z is all points on the 45 deg line RAISED by 1 unit, which line passes thru the points (-1+0i) & (0+i).
In parametric form, this is (0+i) + t( (0+i)-(-1+0i) ) = i + ti + 1 = 1 + i(t+1), for t>0.

over
Автор

a+(a+1)i for a>0. -> y=x+1 for x>0.

TheLukeLsd
Автор

There is two cases
Let the affixes M(Z), A(i)
The expression becomes
First case:
Arg(Z-i)=(pi)/4+ k(pi), k is an entiger.
The locus is a straight line passing by A(i) and it does not contains A(i) .with angle measure equal:
(pi)/4+k(pi), k is entiger.

Case two:
Arg(Z-i)=(pi)/4+k(2pi), k entiger.
The locus is half of straight line passing by A(i) and it does not contains A(i).
with angle measure equal:
(pi)/4+k(2pi), k is an entiger.

aekben
Автор

note:arg(z)=arctan(b/a)
arctan((b-1)/a)=π/4
(b-1)/a=tan(π/4)=1
b-1=a

Why-kb_