Expected square of a random unit complex number

Let $Z$ be a uniformly random point on the unit circle in the complex plane ( $|Z| = 1$ ). Compute $\mathbb{E}[Z^2]$ .

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Write $Z=e^{i\theta}$ , $\theta\sim\text{Uniform}(0,2\pi)$ , so $Z^2=e^{2i\theta}$ .
Averaging $e^{2i\theta}$ over a full period gives $0$ .

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