簡約 (2xy+iy)^2

解

簡約

(2 x y + i y)^{2}

(4 x^{2} y^{2} - y^{2}) + 4 x y^{2} i

解答ステップ

(2 x y + i y)^{2}

完全平方式を適用する:

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

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

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

(2 x y)^{2} = 4 x^{2} y^{2}

2 \cdot 2 x y i y = 4 x i y^{2}

(i y)^{2} = - y^{2}

= 4 x^{2} y^{2} + 4 x i y^{2} - y^{2}

標準的な複素数形式で書き直す:

(4 x^{2} y^{2} - y^{2}) + 4 x y^{2} i

= (4 x^{2} y^{2} - y^{2}) + 4 x y^{2} i