IGNOU MMTE 5 2026 - Find the zeros and singularities of the function in&n

Question

Find the zeros and singularities of the function $f(z) = \frac{z}{4 \cos^2 z - 1}$ in $|z| \leq 1$ . Also find the residue at the poles

09 Jan 2026

Answer :

Word Count : 237

The given function is [ f(z) = \frac{z}{4\cos^2 z - 1} = \frac{z}{(2\cos z - 1)(2\cos z + 1)}. ] Step 1: Find zeros of (f(z)) The zeros occur when the numerator (z = 0). So, the only zero is: [ z = 0. ] Step 2: Find singularities (poles) Singularities occur when the denominator (4\cos^2 z - 1 = 0), i.e., [ 4\cos^2 z - 1 = 0 \implies \cos^2

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