# GATE Questions & Answers of Complex variables Civil Engineering

#### Complex variables 9 Question(s)

Newton-Raphson method is to be used to find root of equation $3x-{e}^{x}+\mathrm{sin}x=0$ If the initial trial value for the root is taken as 0.333, the next approximation for the root would be _________

(note: answer up to three decimal)

Consider the following complex function:

$\mathrm{f}\left(\mathrm{z}\right)=\frac{9}{\left(\mathrm{z}-1\right){\left(\mathrm{z}+2\right)}^{2}}$

Which of the following is one of the residues of the above function ?

Given $i=\sqrt{-1}$ , the value of the definite integral, $\mathrm I=\int\limits_0^{\pi/2}\frac{\cos\;x\;+\;i\;\sin\;x}{\cos\;x\;-\;i\;\sin\;x}dx$ is :

$z=\frac{2-3i}{-5+i}$ can be expressed as

The infinite series corresponds to

For an analytic function,f(x+iy)=u(x,y)+iv(x,y), u is given by u=3x2-3y2. The expression for v, considering K to be a constant is

The analytic function $f\left(z\right)=\frac{z-1}{{z}^{2}+1}$ has singularities at

The analytic function $f\left(z\right)=\frac{z-1}{{z}^{2}+1}$ has singularities at
The value of the integral $\underset{C}{\int}\frac{\cos\left(2\mathrm{\pi z}\right)}{\left(2z-1\right)\left(z-3\right)}dz$ (where C is a closed curve given by |z| = 1) is