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

[Logarythmic]

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.

 

[Office_Shredder]

Start off by substituting v=x², and try to go from there

 

[TD]

Or swith to an easier, but equivalent, representation of the complex number z (think exponential/polar/...)

 

[benorin]

Hint: $w^2+1=(w+i)(w-i)$

 

[loom91]

Write x^4 = -1 and try to follow what you think is the simplest path without involving anything fancy.

 

[dextercioby]

Well, use the decomposition

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

Daniel.