I have a problem about complex number.

Question

Let z=7e^(7*pi*i/4) .

Write z, z^4, z^7, z^(-2) in the form a + b i

I have no idea how to do it. Any hints will be appreciated.

Answer 1

z=7e^(7*pi*i/4)

z^4 = 7^4 e^(7*pi*i)

And then you use that
e^(i theta) = cos(theta) + i sin(theta)