化简 (x-i*y)^2

解答

化简

(x - i \cdot y)^{2}

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

求解步骤

(x - i y)^{2}

使用完全平方公式:

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

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

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

- 2 x i y = - 2 x y i

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

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

Rewrite in standard complex form:

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

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

e x p an d \frac{x ( 1 - 9 x ) ( 3 x + 2 )}{2 ( 3 x + 1 ) ( 3 x - 1 ) ( x + 7 )}

e x p an d 6 (\frac{6}{12} + \frac{8}{12} + \frac{9}{12})

e x p an d cos (2) (t - \frac{π}{2})

e x p an d (A e^{t} - B e^{- t})^{2}

e x p an d A (5, - 5) Y B (8, 3)