Question

The value of the integral \[ \oint_{|z|=2}\frac{\cos\left(\dfrac{z}{2}\right)}{z^3}\,dz \] is ____.

• A. \(\pi i\)
• B. \(-\pi i\)
• C. \(2\pi i\)
• D. \(-2\pi i\)

Hint:

For integrals of the form \[ \oint\frac{f(z)}{z^{n+1}}\,dz, \] use \[ \boxed{ \frac{2\pi i}{n!}f^{(n)}(0). } \] Always verify the question statement if the computed value differs from the answer key.

Answer 1

The Correct Option is B