Find the Laurent series expansion of the following functions about the given points $z = z_0$ or in the given region (specify the region in which the expansion is valid wherever it is necessary). \frac{1}{z^2 + 1} in the neighborhood of $z = -i$ $f(z) = \frac{3}{2 + z - z^2}$
Added by Mar C.
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To do this, we can perform a partial fraction decomposition. Let's first complete the square in the denominator: $$z^2 + 2z + 2 = (z + 1)^2 + 1$$ Now, we can rewrite the function as: $$f(z) = \frac{3}{(z + 1 + i)(z + 1 - i)}$$ Show more…
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