a+bi-1/(a+bi)=4+4i

解

a + bi - \frac{1}{a + bi} = 4 + 4 i

(a = - 0.12864 \dots, a = 4.12864 \dots, b = 0.12087 \dots b = 3.87912 \dots)

解答ステップ

a + bi - \frac{1}{a + bi} = 4 + 4 i

以下で両辺を乗じる:

a + bi

a (a + bi) + bi (a + bi) - \frac{1}{a + bi} (a + bi) = 4 (a + bi) + 4 i (a + bi)

拡張

(a^{2} - b^{2} - 1) + 2 iab = (4 a - 4 b) + i (4 a + 4 b)

複素数は, その実数部と虚数部が等しい場合にのみ等しくなるequation系として書き換える:

[a^{2} - b^{2} - 1 = 4 a - 4 b 2 ab = 4 a + 4 b]

[a^{2} - b^{2} - 1 = 4 a - 4 b 2 ab = 4 a + 4 b] : (a = - 0.12864 \dots, a = 4.12864 \dots, b = 0.12087 \dots b = 3.87912 \dots)

(a = - 0.12864 \dots, a = 4.12864 \dots, b = 0.12087 \dots b = 3.87912 \dots)