Question
Find the zeros and singularities of the function in
. Also find the residue at the poles
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 ______ _____ _______ _______ ___.
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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 ______ _____ _______ _______ ___.
_______ __________ ___ ______ ______ ___ ________ ______.
_________ ____ ________ _______ ______ _____.
_____ ___ ________ ___ ___ _____ ________ ________ ______ __________.
_________ ______ ____ _____ _____ _____ _________ _________ ________ _____.
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____ ____ ______ ________ ___.
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_________ ____ _________ _____.
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