GATE Papers >> EEE >> 2019 >> Question No 14

Question No. 14

Which one of the following functions is analytic in the region |z| $\leq$ 1?

Answer : (B) $\frac{z^2-1}{z+2}$

Solution of Question No 14 of GATE 2019 EEE Paper

Given region is $\left|\mathrm z\right|\leq1;$ which represents the region inside and on the unit circle |z| = 1

The functions given in the options A, C, D are not analytic functions in the region $\left|\mathrm z\right|\leq1;$ Since the singular points -j(0.5), 0.5, 0 lies inside |z| = 1.

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

⇒ z =-2 is the singular point but this is lies outside |z|=1

$\therefore\frac{\mathrm z^2-1}{\mathrm z+2}$ is analytic in the region $\left|\mathrm z\right|\leq1$.