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Express $(5-3i)^{3}$ in the form $a+ib$.

The equation of the smallest degree with real coefficients having $1 + i$ as one of the roots is

$\sum\limits_{n=1}^{50} i^{(2n-1)!}$ is equal to (where $i = \sqrt{-1}$)

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Let $z \in \mathbb{C}$ with $\operatorname{Im}(z)=10$ and it satisfies $\frac{2z-n}{2z+n}=2i-1$, where $i=\sqrt{-1}$, for some natural number $n$. Then:

${\left( \frac{1 + i}{1 - i} \right)^2} + {\left( \frac{1 - i}{1 + i} \right)^2}$ is equal to

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