# GATE Questions & Answers of Complex variables Electrical Engineering

#### Complex variables 11 Question(s)

Let S be the set of points in the complex plane corresponding to the unit circle. (That is, $S=\left\{z:\left|z\right|=1\right\}$). Consider the function $f\left(z\right)=z{z}^{*}$ where z* denotes the complex conjugate of z. The $f\left(z\right)$ maps S to which one of the following in the complex plane

The line integral of function F = yzi, in the counterclockwise direction, along the circle x2+y2 = 1 at z = 1 is

All the values of the multi-valued complex function ${1}^{i}$, where $i=\sqrt{-1}$,are

Integration of the complex function $f\left(z\right)=\frac{{z}^{2}}{{z}^{2}-1}$,in the counterclockwise direction, around $\left|z-1\right|=1$,is

Square roots of $-i$, where $i=\sqrt{-1}$ are

$\int \frac{{z}^{2}-4}{{z}^{2}+4}dz$ evaluated anticlockwise around the circle $\left|z-i\right|=2$ ,where $i=\sqrt{-1}$, is

If $x=\sqrt{-1},$ then the value of xx is

Given

f(z)= $\frac{1}{z+1}-\frac{2}{z+3}$. If C is a counterclockwise path in the z-plane such that $\left|z+1\right|=1$, the value of $\frac1{2\pi j}\oint_cf\left(z\right)dz$ is

A point Z has been plotted in the complex plane, as shown in figure below.

The plot of the complex number $y=\frac{1}{Z}$ is

The period of the signal $x\left(t\right)=8\mathrm{sin}\left(0.8\mathrm{\pi }t+\frac{\mathrm{\pi }}{4}\right)\phantom{\rule{0ex}{0ex}}$ is
The value of $\oint\limits_C\frac{dz}{\left(1+z^2\right)}$ where C is the contour |z - i/2| = 1 is