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

Question No. 14 EEE | GATE 2019

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 $.

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