Complex roots

1. Aug 18, 2006

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.

2. Aug 18, 2006

Office_Shredder

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

3. Aug 18, 2006

TD

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

4. Aug 20, 2006

benorin

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

5. Aug 21, 2006

loom91

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

6. Aug 21, 2006

dextercioby

Well, use the decomposition

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

Daniel.