Question

The value of the integral ${\oint }_C\frac{-3z+4}{(z^2+4z+5)}dz$ wherer $c$ is the circle $|Z|=1$ is given by

• A. $0$
• B. $1/10$
• C. $4/5$
• D. $1$

Answer 1

The correct option is A $0$

$I={\oint }_C\frac{-3z+4}{(z^2+4z+5)}dz,c:|z|=1$
$z=-2\pm i$ are simple poles which lies outside $c$, so,
$I=0$ (By Cauchy integral theorem)