極形式で積・商を計算する（A）

絶対値は掛け算・割り算，偏角は足し算・引き算になる． \[ \alpha\beta=6\left\{\cos\left(\frac{\pi}{4}+\frac{\pi}{12}\right)+i\sin\left(\frac{\pi}{4}+\frac{\pi}{12}\right)\right\}=6\left(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\right)=3+3\sqrt{3}i \] \[ \frac{\alpha}{\beta}=\frac{2}{3}\left\{\cos\left(\frac{\pi}{4}-\frac{\pi}{12}\right)+i\sin\left(\frac{\pi}{4}-\frac{\pi}{12}\right)\right\}=\frac{2}{3}\left(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6}\right)=\frac{\sqrt{3}}{3}+\frac{1}{3}i \]