i(x)=(x^2-16)/(x-6)

解

i (x) = \frac{x ^{2} - 16}{x - 6}

x = 4.39241 \dots - \frac{- 2.78482 \dots + 20.92849 \dots}{2} i, x = - 1.39241 \dots - \frac{8.78482 \dots - 20.92849 \dots}{2} i

解答ステップ

i (x) = \frac{x ^{2} - 16}{x - 6}

代用

x = a + bi

i (a + bi) = \frac{( a + bi ) ^{2} - 16}{a + bi - 6}

以下で両辺を乗じる:

a - 6 + ib

i (a + bi) (a - 6 + ib) = \frac{( a + bi ) ^{2} - 16}{a + bi - 6} (a - 6 + ib)

拡張

(- 2 ab + 6 b) + i (a^{2} - b^{2} - 6 a) = (a^{2} - b^{2} - 16) + 2 iab

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:

[- 2 ab + 6 b = a^{2} - b^{2} - 16 a^{2} - b^{2} - 6 a = 2 ab]

[- 2 ab + 6 b = a^{2} - b^{2} - 16 a^{2} - b^{2} - 6 a = 2 ab] : (a = 4.39241 \dots, a = - 1.39241 \dots, b = - \frac{- 2.78482 \dots + 20.92849 \dots}{2} b = - \frac{8.78482 \dots - 20.92849 \dots}{2})

代用を戻す

x = a + bi

x = 4.39241 \dots - \frac{- 2.78482 \dots + 20.92849 \dots}{2} i, x = - 1.39241 \dots - \frac{8.78482 \dots - 20.92849 \dots}{2} i