Question

By using Cauchy integral theorem, the value of an integral (integration being taken in counter clock wise direction) $\oint \frac{z^{3}-4}{3z-i} dz$; is:

• A. 1
• B. 0
• C. $\frac{2\pi}{81}-\frac{4\pi i}{3}$
• D. $\frac{2\pi}{81}-\frac{8\pi i}{3}$

Hint:

Always ensure the coefficient of $z$ in the denominator is 1 before applying Cauchy's Integral Formula. Factoring out the constant (like the 3 in $3z-i$) is a common first step.

Answer 1

The Correct Option is D