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Express the given complex number in the form $a+ib$: $\left(\frac{1}{3}+3i\right)^{3}$

$\frac{1 - 2i}{2 + i} + \frac{4 - i}{3 + 2i} = $

Express the following in the form of $a+bi$:
$(-5i) \left(\frac{1}{8}i\right)$

$i^2+i^3+\ldots+i^{4000}=$

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:

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