Originally Posted by

**Quacky** I have absolutely no idea where this question should go, so please feel free to move it to the correct subforum.

a)If $\displaystyle z = cos\theta + i sin\theta$, use de Moivre's theorem to show that $\displaystyle \displaystyle z^n + \frac{1}{z^n} = 2cos (n\theta)$

b) Express $\displaystyle (z^2 + \frac{1}{z^2})^3$ In terms of $\displaystyle Cos{6\theta}$ and $\displaystyle Cos{2\theta}$

Part a) I have done correctly, but part b) Is confusing me. My working so far:

$\displaystyle (z^2 + \frac{1}{z^2})^3$

$\displaystyle = [2Cos(2\theta)]^3$

$\displaystyle =2^3(Cos(2\theta))^3$

$\displaystyle =8(Cos(2\theta))^3$

Then I hit a wall. At first glance, I try to say '$\displaystyle =8Cos6\theta$' but that doesn't fit the question. I see that I have to use the theorem in some way, but I have no idea on the correct approach from here.