If $z\in \mathbb C$ calculate: $$\Bigl|\frac{1}{n^z}\Bigr|$$ with n a natural number.
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2026-04-04 22:03:45.1775340225
Calculate $\bigl|\frac{1}{n^z}\bigr|$.
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Apparently, $n^z$, for $n\in\mathbb N$, is defined as $$ n^z=\mathrm{e}^{z\log n}=\mathrm{e}^{\log n\,(\mathrm{Re}\,z+i\,\mathrm{Im}\,z)}, $$ and hence $$ \lvert n^z\rvert=\mathrm{e}^{\log n\,(\mathrm{Re}\,z)}. $$