Understanding and Calculating Residues for 1/(1+z²+z⁴)

[oddiseas]

Homework Statement

computing the residue;
1/(1+z²+z⁴)

Homework Equations

Can someone explain to me what a residue is and how to calculate it! Is it simply the discontinuities of the function?

The Attempt at a Solution

 

[Gregg]

Its the co-efficient of the series expansion term at the singularity I think.

 

[Hurkyl]

Doesn't your complex analysis text define it?

 

[HallsofIvy]

Its the co-efficient of the series expansion term at the singularity I think.

The residue is the coefficient of (x- x₀)^-1 in a series expansion about the pole.