GATE Questions & Answers of Complex variables Civil Engineering

Newton-Raphson method is to be used to find root of equation 3x-ex+sinx=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:

fz=9z-1z+22

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

Given i=-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=2-3i-5+i can be expressed as

The infinite series 1+x+x22!+x33!+x44!+..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 fz=z-1z2+1 has singularities at

The analytic function fz=z-1z2+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