List of top Engineering Mathematics Questions on Complex Functions asked in TS PGECET

The value of the integral \(\displaystyle\oint_{C}\frac{z e^{-z}}{(z-1)(z-2)}\,dz\) where \(C:|z|=\dfrac{3}{2}\) is

For which values of \(k\) does the function \(f(z)=\left(x^3-3xy^2\right)+i\left(kx^2y-y^3\right)\) become analytic?

Find the residue of the function \[ f(z) = \frac{1}{z^2 + 1} \] at the pole $z = i$.

The number of non-differentiable points for the function $f(x) = \min\left\{x - \lfloor x \rfloor, 1 - x + \lfloor x \rfloor\right\}$ in $(-2, 2)$ is ($\lfloor x \rfloor$ represents integral part of $x$)