- #1
Shackleford
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Homework Statement
Calculate ∫C [itex]\frac{dz}{z(z+a)}[/itex] where C is the unit disk Δ(1) with counterclockwise orientation where a is a complex number with |a| < 1.
Homework Equations
∫L [itex]\frac{dz}{(z-p)}[/itex]= 2πiν(L,p)
The Attempt at a Solution
Using partial fraction decomposition,
∫C [itex]\frac{dz}{z(z+a)}[/itex] = ∫C[itex]\frac{-1/a}{z} + \frac{1/a}{(z+a)}[/itex] = (-1/a)2πi + (1/a)2πi = 0