簡約 (3x+4i)^2

解

簡約

(3 x + 4 i)^{2}

(9 x^{2} - 16) + 24 x i

解答ステップ

(3 x + 4 i)^{2}

完全平方式を適用する:

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

(3 x + 4 i)^{2} = (3 x)^{2} + 2 \cdot 3 x \cdot 4 i + (4 i)^{2}

= (3 x)^{2} + 2 \cdot 3 x \cdot 4 i + (4 i)^{2}

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

2 \cdot 3 x \cdot 4 i = 24 x i

(4 i)^{2} = - 16

= 9 x^{2} + 24 x i - 16

標準的な複素数形式で書き直す:

(9 x^{2} - 16) + 24 x i

= (9 x^{2} - 16) + 24 x i