Question

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

07 Feb 2024
Answer :
Word Count : 345

To find the zeros and singularities of the function \( f(z) = \frac{z}{4\cos^2(z) - 1} \) in \( |z| \leq 1 \), we need to analyze where the denominator becomes zero, since division by zero is not defined.

The function \( f(z) \) will have singularities where the denominator \( 4\cos^2(z) - 1 \) equals zero. The cosine function has zeros at \( z = \frac{\pi}{2} + k\pi \) ____ _________ __________ ___ ____ _____ ___ ______ _______ ____ _____.
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