GATE Questions & Answers of Cauchy-Riemann equations

What is the Weightage of Cauchy-Riemann equations in GATE Exam?

Total 3 Questions have been asked from Cauchy-Riemann equations topic of Complex variables subject in previous GATE papers. Average marks 1.67.

$F\left(z\right)$ is a function of the complex variable $z=x+iy$ given by

$F\left(z\right)=i\;z\;+\;k\;Re\;\left(z\right)+i\;Im\left(z\right)$.

For what value of k will $F\left(z\right)$ satisfy the Cauchy-Riemann equations?

If z is a complex variable, the value of $\int\limits_5^{3i}\frac{dz}z$ is
The integral $\oint f\left(z\right)dz$ evaluated around the unit circle on the complex plane for $f\left(z\right)=\frac{\mathrm{cos}z}{z}$ is