$f(z)= \dfrac{2z+3i}{z^{2}+1/4}$, $C$ is the unit circle centered at zero.
Though the answer is $12\pi$, but my answer is coming to be $4\pi i$ If we decompose it into partial fractions then $f(z)$ reduces to $\dfrac{4}{z-\frac{i}{2}} - \dfrac{2}{z+ \frac{i}{2}}$
Applying Cauchy Integral formula, the first part integrates to $8\pi i $ and the second part reduces to $4\pi i$. Thus my answer, but the actual answer is otherwise
Help appreciated, Soham