anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Here is what I got up till now.
1 Attachment
anonymous
  • anonymous
Polar Form .....
anonymous
  • anonymous
Cosx + i sinx = e^(ix) == Euclear Theorem

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
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.
anonymous
  • anonymous
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.
anonymous
  • anonymous
Do I am on the right way (on the picture)? I just need to work in the radius?
anonymous
  • anonymous
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.
anonymous
  • anonymous
k, I will try to do that. Thank you for your time and help, AnimalAin.
anonymous
  • anonymous
You should end up with \[z_3 = rs(\cos (\theta + \gamma)+i \sin(\theta + \gamma)\]
anonymous
  • anonymous
Have fun. Do math every day.
anonymous
  • anonymous
I´ll try ;)
anonymous
  • anonymous
Thx, I just did the calculation and it worked out just fine. Thank you for your help, AnimalAin. Now I can claim VICTORY! ;)

Looking for something else?

Not the answer you are looking for? Search for more explanations.