Question

Use Demoivres Theorem to find (-square root 3 +i)^6

Answer 1

A) -64

Explanation:

Edge 2021

Answer 2

`z=(-√(3)+i)^6` = -64

Explanation:

You have the following complex number:

`z=(-√(3)+i)^6` (1)

The Demoivres theorem stables the following:

`z^n=r^n(cos(n\theta)+i sin(n\theta))` (2)

In this case you have n=6

In order to use the theorem you first find r and θ, as follow:

`r=√(3+1)=2\\\\\theta=tan^(-1)((1)/(√(3)))=30\°`

Next, you replace these values into the equation (2) with n=6:

`z^6=(2)^6[cos(6*30\°)+isin(6*30\°)]\\\\z^6=64[-1+i0]=-64`

Then, the solution is -64