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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.
 one year ago
 one year 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.
 one year ago
 one year ago

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TomLikesPhysicsBest ResponseYou've already chosen the best response.1
Here is what I got up till now.
 one year ago

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

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
Aw, 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.
 one year ago

AnimalAinBest ResponseYou've already chosen the best response.1
Let 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.
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
Do I am on the right way (on the picture)? I just need to work in the radius?
 one year ago

AnimalAinBest ResponseYou've already chosen the best response.1
Put 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.
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
k, I will try to do that. Thank you for your time and help, AnimalAin.
 one year ago

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

AnimalAinBest ResponseYou've already chosen the best response.1
Have fun. Do math every day.
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
Thx, I just did the calculation and it worked out just fine. Thank you for your help, AnimalAin. Now I can claim VICTORY! ;)
 one year ago
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