Question

The values of the integral $\frac{1}{2\pi j}{\oint }_c\frac{e^z}{z-2}dz$ along a closed contour $c$ in anti-clockwise direction for
(i) the point $z_o=2$ inside the contour $c$, and
(ii) the point $z_o=2$ outside the contour $c$, respectively, are

• A. (i) $2.72,$ (ii) $0$
• B. (i) $7.39,$ (ii) $0$
• C. (i) $0,$ (ii) $2.72$
• D. (i) $0,$ (ii) $7.39$

Answer 1

The correct option is B (i) $7.39,$ (ii) $0$

(i) $\frac{1}{2\pi j}{\oint }_c\frac{e^z}{z-2}dz=\frac{1}{2\pi j}2\pi jf\left(z\right)=e^2=7.39$

(ii) $\frac{1}{2\pi j}{\oint }_c\frac{e^z}{z-2}=0$