A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
I have two complex numbers:
z1=a+ib and z2=c+id
I am supposed to write them in that form: z=(rcos(theta), rain(theta)).
Using that form I need to prove that theta of z3 (z3=z1*z2) is theta of z1 + theta of z2.
Using the e^itheta from of complex numbers that would be simple problem but in that component form I can not find a way to prove that.
 2 years ago
I have two complex numbers: z1=a+ib and z2=c+id I am supposed to write them in that form: z=(rcos(theta), rain(theta)). Using that form I need to prove that theta of z3 (z3=z1*z2) is theta of z1 + theta of z2. Using the e^itheta from of complex numbers that would be simple problem but in that component form I can not find a way to prove that.

This Question is Closed

TomLikesPhysics
 2 years ago
Best ResponseYou've already chosen the best response.1Here is what I got up till now.

Yahoo!
 2 years ago
Best ResponseYou've already chosen the best response.0Cosx + i sinx = e^(ix) == Euclear Theorem

TomLikesPhysics
 2 years ago
Best ResponseYou've already chosen the best response.1Aw, I think I am not allowed to use the "e" from. I am supposed to write the complex number as a vector in the form (radius*cos(angle) , radius*sin(angle)). Writing it like that I must prove that the angles add if I multiply two complex numbers.

AnimalAin
 2 years ago
Best ResponseYou've already chosen the best response.1Let a= r cos theta, b= r sin theta, c= s sin gamma, d= s cos gamma, r= (a^2+b^2)^1/2, s=(c^2+d^2)^1/2 Substitute into your equation, throw a few trig substitutions at it, and declare victory.

TomLikesPhysics
 2 years ago
Best ResponseYou've already chosen the best response.1Do I am on the right way (on the picture)? I just need to work in the radius?

AnimalAin
 2 years ago
Best ResponseYou've already chosen the best response.1Put the substitutions above into the equation you have for Z3, and look for a sum of angles trig identity to work backwards to your desired result.

TomLikesPhysics
 2 years ago
Best ResponseYou've already chosen the best response.1k, I will try to do that. Thank you for your time and help, AnimalAin.

AnimalAin
 2 years ago
Best ResponseYou've already chosen the best response.1You should end up with \[z_3 = rs(\cos (\theta + \gamma)+i \sin(\theta + \gamma)\]

AnimalAin
 2 years ago
Best ResponseYou've already chosen the best response.1Have fun. Do math every day.

TomLikesPhysics
 2 years ago
Best ResponseYou've already chosen the best response.1Thx, I just did the calculation and it worked out just fine. Thank you for your help, AnimalAin. Now I can claim VICTORY! ;)
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.