# Partial fractions with complex numb

1. Jul 2, 2013

### Miike012

How do I turn 1/(x4+1) into partial fractions?

This is what I did. Let me know if this is correct

1/(x4+1) = 1/[(x^2+i)(x^2-i)] = (Ax+B)/(x2+i) + (Cx + D)/(x2-1)

Then I set x = 0

1 = (D-B)i .. My first equation would be D-B = 0.

Is that correct so far?

Last edited: Jul 2, 2013
2. Jul 2, 2013

### Infrared

No need to use complex numbers. $x^4+1=(x^2+1)^2-2x^2=(x^2+1+\sqrt{2}x)(x^2+1-\sqrt{2}x)$

This is a very messy integral to do by hand, by the way.

Last edited: Jul 2, 2013