Homework Help: Complex Variables (Finding complex roots)

1. Feb 11, 2012

Polamaluisraw

1. The problem statement, all variables and given/known data
Find all solutions to (z2+1)2=-1

3. 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!

2. Feb 11, 2012

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.

3. Feb 11, 2012

Polamaluisraw

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

4. Feb 11, 2012

Polamaluisraw

got it,

±21/4*exp(i3$\pi$/8)
21/4*exp(i5$\pi$/8)

thank you again

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