What Are the Roots of z^n = -1 in Complex Numbers?

sara_87
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Homework Statement



What are the roots of

z^n = -1

Homework Equations





The Attempt at a Solution



are they

e^{\frac{2\pi k i}{n}-\frac{i \pi}{n}}

?
 
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sounds reasonable
 
if by k you mean "all integer values k in [0,n[" then yes, that is correct, which in turn implies n nth roots.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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