簡約 (x+iy)^3+(x+iy)^2

解

簡約

(x + i y)^{3} + (x + i y)^{2}

(x^{3} - 3 x y^{2} + x^{2} - y^{2}) + (3 x^{2} y - y^{3} + 2 x y) i

解答ステップ

(x + i y)^{3} + (x + i y)^{2}

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

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

= x^{3} + 3 x^{2} y i - 3 x y^{2} - i y^{3} + x^{2} + 2 x y i - y^{2}

標準的な複素数形式で書き直す:

(x^{3} - 3 x y^{2} + x^{2} - y^{2}) + (3 x^{2} y - y^{3} + 2 x y) i

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