Complex Variables (Finding complex roots)

  • #1

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!
 

Answers and Replies

  • #2
LCKurtz
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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
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!
 
  • #4
got it,

±21/4*exp(i3[itex]\pi[/itex]/8)
21/4*exp(i5[itex]\pi[/itex]/8)

thank you again
 

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