1. Complex no.

The area of Region formed by the point $\displaystyle P(z)$ lying inside the incircle of hexagon and satisfying

$\displaystyle \displaystyle \frac{\pi}{3}\leq \arg(z)\leq \frac{5\pi}{6}$ is $\displaystyle \frac{m}{n}\pi$.

Where $\displaystyle m$ and $\displaystyle n$ are relatively prime natural numbers. then $\displaystyle m+n$ is

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