Question

How to raise the number to the indicated power and express in trigonometric notation.

(2(cos3/7π + i sin3/7π))²

Answer 1

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

We have
`r=2` and
`\theta=(3)/(7)\pi`
So we get:

`(2(\cos(3)/(7)\pi+i\sin(3)/(7)\pi))^(2)=4(\cos(6)/(7)\pi+i\sin(6)/(7)\pi)`