Recent questions tagged cauchys-integral-theorem

Let $f\left ( z \right )=\dfrac{1}{z^{2}+6z+9}$ defined in the complex plane. The integral $\oint _{c}\:f\left ( z \right )dz$ over the contour of a circle $\text{c}$ wit...

Let $f(z)=\frac{1}{z+a},a>0.$ the value of the integral $\oint f(z)dz$ over a circle $C$ with center $(-a,0)$ and radius $R>0$ evaluated in the anti-clockwise direction i...

The value of the integral $\displaystyle{}\frac{1}{2\pi j}\int_c \frac{Z^2+1}{Z^2-1}dz$ where $z$ is a complex number and $C$ is a unit circle with center at $1+0j$ in th...

The value of $\oint \frac{1}{Z^2} dZ,$ where the contour is the unit circle traversed clockwise, is$-2\pi i$$0$$2\pi i$$4\pi i$

Given $f(z)=\frac{1}{z+1}-\frac{2}{z+3}.$ If $C$ is a counterclockwise path in the $z$-plane such that $|z+1|=1,$ the value of $\frac{1}{2\pi j}\oint_cf(z)dz$ is$-2$$-1$$...