化简 (x-4-3i)^2

解答

化简

(x - 4 - 3 i)^{2}

(x^{2} - 8 x + 7) + (24 - 6 x) i

求解步骤

(x - 4 - 3 i)^{2}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

(x - 4 - 3 i)^{2} = (x - 4 - 3 i) (x - 4 - 3 i)

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

打开括号

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

化简

xx + x (- 4) + x (- 3 i) - 4 x - 4 (- 4) - 4 (- 3 i) - 3 i x - 3 i (- 4) - 3 i (- 3 i) : 24 i + x^{2} - 8 x - 6 x i + 7

= 24 i + x^{2} - 8 x - 6 x i + 7

Rewrite in standard complex form:

(x^{2} - 8 x + 7) + (24 - 6 x) i

= (x^{2} - 8 x + 7) + (24 - 6 x) i

e x p an d (23)^{2} + 2^{2}

e x p an d (50 - \frac{q}{2} = \frac{9}{4} 300 - 4 p) (75 - \frac{q}{4})

e x p an d, 5 (5 - x) + 3 (5 - x)^{2} + 3 x + 2 x^{3}

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

e x p an d d x (\frac{1}{15} arcsec (\frac{x}{5}) + c)