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Which one of the following functions is analytic in the region |z| ≤ 1?

1. (z²−1)/z
2. (z²−1)/(z+2)
3. (z²−1)/(z−0.5)
4. (z²−1)/(z+j0.5)

Correct answer: (z²−1)/(z+2)

Solution

The function (z²−1)/(z+2) is analytic in the region |z| ≤ 1 because it is a rational function with no singularities or poles within that region, as the denominator z+2 does not equal zero for any z such that |z| ≤ 1.

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