カテゴリー: 複素数

\[ \Arg z^{-1}=-\Arg z+2\pi\delta_{\pi,\Arg\left(z\right)} \]

\[ z\pm\overline{z}=2H\left(\pm1\right)\Re z+2iH\left(\mp1\right)\Im z \]

\[ \Arg\left(\alpha\right)+\Arg\left(\beta\right)=?\Arg\left(\alpha\beta\right) \]

\[ \pv\alpha^{\beta}\pv\alpha^{\gamma}=\pv\alpha^{\beta+\gamma} \]

\[ \log\alpha^{\beta}=\beta\log\alpha+\log1 \]

\[ \alpha^{\beta}=\left|\alpha\right|^{\Re\left(\beta\right)}e^{-\Im\left(\beta\right)\arg\alpha}e^{i\left(\Im\left(\beta\right)\ln\left|\alpha\right|+\Re\left(\beta\right)\arg\alpha\right)} \]

\[ \log z=\Log z+\log1 \]

\[ e^{\alpha+\beta}=e^{\alpha}e^{\beta} \]

\[ \alpha^{\beta}=e^{\beta\log\alpha} \]