Question

How do you simplify `[2(cos 135degrees+i sin 135 degrees)]^4`?

Answer 1

You may use the de Moivre's Theorem:

`z=r[cos(theta)+isin(theta)] =>z^n=r^n[cos(ntheta)+isin(ntheta)]`

In your case you get:

`z^4=2^4[cos(4*135°)+isin(4*135°)]=`

`=16[cos(540°)+isin(540°)]`

(which is `=-16` in rectangular form)