If $\displaystyle z_1, z_2, ... z_n$ are complex, prove that $\displaystyle \mid z_1 + z_2 + ... + z_n \mid \leq \mid z_1 \mid + \mid z_2 \mid + ... + \mid z_n \mid$.
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This looks to be $\displaystyle n$ applications of the Triangle Inequality..
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