CSIR NET MATHEMATICS DEC2016 || COMPLEX ANALYSIS || COMPLETE SOLUTION || Part C.

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Complex analysis: radius of convergence, analytic function, singularity, complex roots, Schwartz lemma, continuity.
Solution of december 2016 .
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In problem 79 finding zeros of (1-e^z) sinz alone is not enough to say that they are simple pole. Showing derivative of (1-e^z) sinz doesn't get vanishes on those zeros will say that those zeros are simple poles of the function

monikad

Mam q.no 81 12complex roots (option d) also right answer ?

rpriyadharshini

In question 79 correct options will be 1 and 3.

SaddamHussain-jsut

Mam in 82 question in first option u did in wrong way i think bcz if g holomorphic take z-1 and when u will do g/z then it has sing at z =0 so g/z is not analytic

First option is correct for correct approch of this option is that h(z) = g'(0) and g is entire and nth derivative is also entire so h is entire so first correct

If i am wrong please correct me

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