Which one of the following function is analytic in the region $| Z | \leq 1$ ?

\frac{z^{2} - 1}{z}

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\frac{z^{2} - 1}{z + j 0.5}

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\frac{z^{2} - 1}{z - 0.5}

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\frac{z^{2} - 1}{z + 2}

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Solution

The correct option is D $\frac{z^{2} - 1}{z + 2}$
In option $1, 2$ and $3$ singularities lying inside the contour.
In option $4$ singularity $z = - 2$ lying outside the contour $z = 1$ .
So, the function given in option $4$ is analytic in the region $| z | \leq 1$ .

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Which one of the following function is analytic in the region |Z|≤1?

The correct option is D z2−1z+2In option 1,2 and 3 singularities lying inside the contour. In option 4 singularity z=−2 lying outside the contour z=1. So, the function given in option 4 is analytic in the region |z|≤1.

Which one of the following function is analytic in the region $| Z | \leq 1$ ?

The correct option is D $\frac{z^{2} - 1}{z + 2}$
In option $1, 2$ and $3$ singularities lying inside the contour.
In option $4$ singularity $z = - 2$ lying outside the contour $z = 1$ .
So, the function given in option $4$ is analytic in the region $| z | \leq 1$ .