# Complex roots

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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Office_Shredder
Staff Emeritus
Gold Member
Start off by substituting v=x2, and try to go from there

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

benorin
Homework Helper
Gold Member
Hint: $w^2+1=(w+i)(w-i)$

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

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