化简 2(x+iy)^2

解答

化简

2 (x + i y)^{2}

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

求解步骤

2 (x + i y)^{2}

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

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

使用分配律:

m (a + b + c) = ma + mb + m c

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

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

2 \cdot 2 x y i = 4 x y i

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

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

Rewrite in standard complex form:

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

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

e x p an d A (- 3, - 4) B (2, 11)

e x p an d (1 - a cos (x))^{2}

e x p an d π (482 - \frac{272 2}{15})

e x p an d 2 (x - 2) + cot (x)

s im pl i f y (3 x - 4) (x + 8)