簡約 (3x-2i)^2

解

簡約

(3 x - 2 i)^{2}

(9 x^{2} - 4) - 12 x i

解答ステップ

(3 x - 2 i)^{2}

完全平方式を適用する:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(3 x - 2 i)^{2} = (3 x)^{2} - 2 \cdot 3 x \cdot 2 i + (2 i)^{2}

= (3 x)^{2} - 2 \cdot 3 x \cdot 2 i + (2 i)^{2}

(3 x)^{2} = 9 x^{2}

- 2 \cdot 3 x \cdot 2 i = - 12 x i

(2 i)^{2} = - 4

= 9 x^{2} - 12 x i - 4

標準的な複素数形式で書き直す:

(9 x^{2} - 4) - 12 x i

= (9 x^{2} - 4) - 12 x i