化简 (x-2)(x-1+i)(x+1-i)

解答

化简

(x - 2) (x - 1 + i) (x + 1 - i)

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

求解步骤

(x - 2) (x - 1 + i) (x + 1 - i)

将

x + 1 - i

改写成标准复数形式:

(x + 1) - i

= (x - 2) (x - 1 + i) ((x + 1) - i)

使用复数算数法则:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= (x - 2) (((x - 1) (x + 1) - 1 \cdot (- 1)) + ((x - 1) (- 1) + 1 \cdot (x + 1)) i)

化简

((x - 1) (x + 1) - 1 \cdot (- 1)) + ((x - 1) (- 1) + 1 \cdot (x + 1)) i : x^{2} + 2 i

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

打开括号

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

展开

(x - 2) \cdot 2 : 2 x - 4

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

e x p an d \frac{x + 10}{( x - 2 ) ( x + 2 )}

e x p an d x^{\frac{1}{4}} (2 x - 2)

s im pl i f y (x - a) (x + a)

e x p an d \frac{d x}{( 7 x + 3 ) ^{2}}

e x p an d (e^{2 x} + e^{- x})^{2}