# Thread: Complex numbers powers can any one help ...

1. ## Complex numbers powers can any one help ...

Let z=3(cos(-1/3*pi)+i sin(-1/3*pi))
What is the modulus of z^3
|z^3| =
Thanks

2. ## Re: Complex numbers powers can any one help ...

Use de Moivre's theorem:

If $z = r(cos (A) + i sin (A))$ then $z^n = r^n(cos (nA) + i sin (nA))$.

3. ## Re: Complex numbers powers can any one help ...

ahh right ,I'd have to find R first right ?
I know on the cartesian plane its |z| = sqrt *a^2+b^2 ...how about in polar form how would I find R ....not sure if my answers right or not ,Thanks

4. ## Re: Complex numbers powers can any one help ...

Originally Posted by bee77
ahh right ,I'd have to find R first right ?
I know on the cartesian plane its |z| = sqrt *a^2+b^2 ...how about in polar form how would I find R ....not sure if my answers right or not ,Thanks
You've been given the complex number in polar form , ie r(cos(A) + i sin(A)) so r = 3