Could anyone help me separate this into partial fractions: $$\frac{\cos(z)}{z^2+1}$$ where $z=x+iy$. I've factored the denominator to get $$\frac{\cos(z)}{(z+i)(z-i)}$$ but I'm not really sure where to go from there. Thanks
2026-03-29 02:10:53.1774750253
Complex partial fractions
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You want to do it without the cosine? $$ \frac{1}{(z+i)(z-i)} = \frac{A}{z+i}+\frac{B}{z-i} $$ where $A,B$ are complex constants. Solve for $A,B$ as in the real case. (But use complex arithmetic.)
.........
Then you can multiply by $\cos(z)$, it does not vanish at $i$ or at $-i$.