Solving 1+x^4=0: Finding the Singular Points

Logarythmic
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I think I've got some minor braindamage or something but i just can't remember how to find the singular points of

1/(1+z^4)

I guess the problem is to solve the equation 1+x^4=0 and get complex roots but this is what I don't remember how to do. Thanks.
 
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Start off by substituting v=x2, and try to go from there
 
Or swith to an easier, but equivalent, representation of the complex number z (think exponential/polar/...)
 
Write x^4 = -1 and try to follow what you think is the simplest path without involving anything fancy.
 
Well, use the decomposition

z^4 +1 =(z^2 +i)(z^2 -i)

Daniel.
 
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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