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受欢迎的代数 >

化简 (x-4)(x-2+3i)(x+2+3i)

解答

化简

(x - 4) (x - 2 + 3 i) (x + 2 + 3 i)

解答

(x - 4) (x^{2} - 13) + (x - 4) \cdot 6 x i

求解步骤

(x - 4) (x - 2 + 3 i) (x + 2 + 3 i)

将

x - 2 + 3 i

改写成标准复数形式:

(x - 2) + 3 i

将

x + 2 + 3 i

改写成标准复数形式:

(x + 2) + 3 i

= (x - 4) ((x - 2) + 3 i) ((x + 2) + 3 i)

使用复数算数法则:

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

= (x - 4) (((x - 2) (x + 2) - 3 \cdot 3) + ((x - 2) \cdot 3 + 3 (x + 2)) i)

化简

((x - 2) (x + 2) - 3 \cdot 3) + ((x - 2) \cdot 3 + 3 (x + 2)) i : (x^{2} - 13) + 6 x i

= (x - 4) ((x^{2} - 13) + 6 x i)

打开括号

= (x - 4) (x^{2} - 13) + (x - 4) \cdot 6 x i

流行的例子

展开 (x^2+y^2+z^2)sqrt(x^2+y^2+z^2)

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

化简 x(200-x/(30))

s im pl i f y x (200 - \frac{x}{30})

展开 ((x+1)(x-1))/x

e x p an d \frac{( x + 1 ) ( x - 1 )}{x}

展开 2/((s-1)(s-2)e^s)

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

展开 (4x^2-4x)*(1+Δx)

e x p an d (4 x^{2} - 4 x) \cdot (1 + Δ x)