Question
Find the zeros and singularities of the function in
. Also find the residue at the poles.
Answer :
Word Count : 236
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The given function is: [ f(z) = \frac{z}{4\cos^2 z - 1}. ] --- Step 1: Find the zeros of (f(z)) Zeros occur when the numerator is zero: [ z = 0. ] Since (|z| \le 1), the only zero is: [ z = 0. ] --- Step 2: Find the singularities of (f(z)) Singularities occur when the denominator is zero: [ 4\cos^2 z - 1 = 0 \implies \cos^2 z = \frac{1}{4} \implies \cos z =
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