Question

If $C$ is a circle of radius $r$ with centre $z_0$ in the complex $z-$plane and if n is a non-zero integer, then
${\oint }_C\frac{dz}{(z-z_o{)}^{n+1}}$ equals

• A. $2\pi nj$
• B. $0$
• C. $\frac{nj}{2\pi }$
• D. $2\pi n$

Answer 1

The correct option is B $0$

${\oint }_C\frac{dz}{(z-z_o{)}^{n+1}}=\frac{2\pi i{f}^n\left(z_o\right)}{n!}=0$
(Using Cauchy integral formula)
Wherer$f\left(z\right)=1\Rightarrow f^n\left(z_0\right)=0$