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JEE-MAIN 2021
16-03-2021 S1
Question
Let $z$ and $\omega$ be two complex numbers such that $\omega=z \bar{z}-2 z+2,\left|\frac{z+i}{z-3 i}\right|=1$ and $\operatorname{Re}(\omega)$ has minimum value. Then, the minimum value of $n \in \mathbb{N}$ for which $\omega^n$ is real, is equal to $\_\_\_\_$ .
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