Complex Line Integral (not too hard)

[Jamin2112]

Homework Statement

∫dz/(z⁴+1) integrated over the curve C₁(1+i)

Homework Equations

The only thing we learned in this chapter is Cauchy's integral formula, so I'm assuming that comes in somehow.

The Attempt at a Solution

∫dz/(z⁴+1) = ∫dz/(z+1+i)(z+1-i)(z-1+i)(z-1-i)

Not bad, eh? Where do I go from here.

 

[susskind_leon]

Look for the poles of your integrand (for which values of z is the denominator 0).
Now find out which of them lie inside of the curve.
Now apply Cauchy's formula.

 

[Jamin2112]

Look for the poles of your integrand (for which values of z is the denominator 0).
Now find out which of them lie inside of the curve.
Now apply Cauchy's formula.

Ah, I see now!