If f(z)=c₀+c₁ z⁻¹, then ∮ (1+f(z))/z dz is given by unit circle

Question

Accepted Answer

(D) 2πj(1+c₀). The integral evaluates the residue of the function (1 + f(z))/z at the pole z=0. The term (1 + f(z)) contributes a constant term of (1 + c₀) to the residue, and since the integral is taken over the unit circle, it results in 2πj times this residue.

If f(z)=c₀+c₁ z⁻¹, then ∮ (1+f(z))/z dz is given by unit circle

Solution

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