Engineering Mat...

What is the value of m for which 2x – x² + my² is harmonic?

Which one of the following functions is analytic over the entire complex plane?

The value of integral \(\mathop \smallint \nolimits_C \frac{{\cos \pi {z^2}}}{{\left( {z - 1} \right)\left( {z - 2} \right)}}dz\) where C : |z| = 3 (Positively oriented) is equal to

Evaluate the contour integral \(\mathop \smallint \nolimits_C f\left( z \right)dz\) using the parametric representations for C, where

The conjugate harmonic function v(x, y) of u(x, y) = In (x² + y²) is

The only function among the following that is analytic, is

While expanding the function \(f\left( z \right) = \frac{{z - 1}}{{z + 1}}\) using Taylor’s series about the point z = 1, what is the coefficient of (z - 1)³ term is

Find the analytic function z = u + iv, if \(2u + v = {e^x}\left( {\cos y-\sin y} \right)\)

The Laurent series expansion of the function \(f\left( z \right) = \frac{1}{{{e^z} - 1}}\) valid in the region 0 < |z| < 2, is given by