Word Count : 395

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To obtain the Taylor series expansion of \[ f(z) = \frac{1}{z^2 + 4} \] about \( z = -i \), we follow these steps: ### Step 1: Express \( f(z) \) in Terms of \( (z + i) \) We rewrite the denominator: \[ z^2 + 4 = (z - i)(z + i) + 3. \] To express it conveniently, set \( w = z _________ ________ ___ ________ ___ ________ ________ _________ ______ ___.
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