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Show that $|\sin z|\geq 1$ at all points on the square with vertices $\pm (N+1/2)\pi\pm(N+1/2)\pi i$, for any positive integer $N$.

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Hint: $|\sinh(y)| = |e^{y} - e^{-y}|/2 >1$ if $|y| > \ln(1 + \sqrt{2})$.

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