The function \frac{Z}{sin \pi {Z}^{2}} of a complex variable Z has

Complex analysis — CSIR Net PYQ (Question 1)

A Complex analysis previous-year question (PYQ) from Mathematical Physics (CSIR Net). Read the question, check the correct answer, then practise the full topic.

Question 1 of 26 · 3.5 marks

The function

\frac{Z}{s inπ Z ^{2}}

of a complex variable

Z

has

1a simple pole at 0 and poles of order 2 at $\pm n$ for $n = 1, 2, 3...$
2a simple pole at 0 and poles of order 2 at $\pm n$ and $\pm i n$ for $n = 1, 2, 3...$
3poles of order 2 at $\pm n, n = 0, 1, 2, 3...$
4poles of order 2 at $\pm n, n = 0, 1, 2, 3...$

Correct answer: Option 2

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