GATE Questions & Answers of Complex variables Electrical Engineering

Let S be the set of points in the complex plane corresponding to the unit circle. (That is, S=z:z=1). Consider the function fz=zz* where z* denotes the complex conjugate of z. The fz 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 1i, where i=-1,are

Integration of the complex function fz=z2z2-1,in the counterclockwise direction, around z-1=1,is

Square roots of -i , where i=-1 are

z2-4z2+4dz evaluated anticlockwise around the circle z-i=2 ,where i=-1, is

If x=-1, then the value of xx is


f(z)= 1z+1-2z+3. If C is a counterclockwise path in the z-plane such that z+1=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=1Z is

The period of the signal xt=8sin0.8πt+π4 is

The value of $\oint\limits_C\frac{dz}{\left(1+z^2\right)}$ where C is the contour |z - i/2| = 1 is