Complex Variables (Finding complex roots)

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Homework Help Overview

The problem involves finding all solutions to the equation (z2+1)2=-1, which is situated within the context of complex variables. The original poster attempts to analyze the polynomial of degree 4 and its geometric interpretation in the complex plane.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the process of finding solutions, with one suggesting the use of square roots of complex numbers. There is also mention of factoring attempts and the realization of missing elements in the original poster's approach.

Discussion Status

The discussion has progressed with participants providing insights and corrections. The original poster acknowledges a mistake and indicates a willingness to continue working on the problem after receiving feedback.

Contextual Notes

There is a focus on the need for clarity in handling complex roots and the implications of the polynomial's degree. The original poster's approach to finding one solution as a means to derive others is noted, along with the potential for multiple interpretations of the problem.

Polamaluisraw
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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!
 
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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.
 
LCKurtz said:
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!
 
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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