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I should make a partial fraction decomposition of the following fraction where $z\in \mathbb{C} $. I am not able to start or do something because I am not able to factorize $z²+4$. Does anybody has any suggestions??

$$\frac{1}{z^{2}+4}$$

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Notice that $z^2+4=(z+2i)(z-2i)$. You can use the normal formula for the roots of a quadratic equation and use that $\sqrt{-1}=i$.

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  • $\begingroup$ Thanks a lot, I was not able to see this by myself :-) $\endgroup$ – zodiac Nov 18 '16 at 23:40
  • $\begingroup$ Make sure that you understand how to find roots of a quadratic equation. If you understand that, it is straightforward to see that this formula still holds for complex quadractic equations. $\endgroup$ – Mathematician 42 Nov 18 '16 at 23:43

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