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Find the multiplicative inverse of the complex number $-i$.

Express the given complex number in the form $a+ib$: $(1-i)^{4}$

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For any two complex numbers $z_{1}$ and $z_{2},$ prove that $\operatorname{Re}(z_{1} z_{2})=\operatorname{Re} z_{1} \operatorname{Re} z_{2}-\operatorname{Im} z_{1} \operatorname{Im} z_{2}.$

If $\frac{3+2i \sin \theta}{1-2i \sin \theta}$ is a real number and $0 < \theta < 2\pi$,then $\theta$ is equal to

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