簡約 (3/5-1/4 i)(2/3+2/5 i)

解

簡約

(\frac{3}{5} - \frac{1}{4} i) (\frac{2}{3} + \frac{2}{5} i)

\frac{1}{2} + \frac{11}{150} i

解答ステップ

(\frac{3}{5} - \frac{1}{4} i) (\frac{2}{3} + \frac{2}{5} i)

複素数の算術規則を適用する:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= (\frac{3}{5} \cdot \frac{2}{3} - (- \frac{1}{4}) \frac{2}{5}) + (\frac{3}{5} \cdot \frac{2}{5} - \frac{1}{4} \cdot \frac{2}{3}) i

簡素化

(\frac{3}{5} \cdot \frac{2}{3} - (- \frac{1}{4}) \frac{2}{5}) + (\frac{3}{5} \cdot \frac{2}{5} - \frac{1}{4} \cdot \frac{2}{3}) i : \frac{1}{2} + \frac{11}{150} i

= \frac{1}{2} + \frac{11}{150} i