Complex Variables (Finding complex roots)

[Polamaluisraw]

Homework Statement

Find all solutions to (z²+1)²=-1

The Attempt at a Solution

I know that because it is a polynomial of degree 4 it is a square inscribed inside of a circle in the complex plane. All i really need is one solution and from that finding the other three is easy. I have tried factoring it numerous ways. the best I get it to is

z²= i -1

thank you!

 

[LCKurtz]

Don't you get $z^2=-1\pm i$? Do you know how to find the square roots of a complex number? That would give you your four roots.

 

[Polamaluisraw]

Don't you get $z^2=-1\pm i$? Do you know how to find the square roots of a complex number? That would give you your four roots.

wow i completely left of the ± that is my problem! Let me work it and ill report back, thank you!

 

[Polamaluisraw]

got it,

±2^1/4*exp(i3$\pi$/8)
2^1/4*exp(i5$\pi$/8)

thank you again