化简-ix(2-i)(5x+6i)

解答

化简

- i x (2 - i) (5 x + 6 i)

(12 x - 5 x^{2}) + (- 10 x^{2} - 6 x) i

求解步骤

- i x (2 - i) (5 x + 6 i)

使用复数算数法则:

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

= - i x ((2 \cdot 5 x - (- 1) \cdot 6) + (2 \cdot 6 - 1 \cdot 5 x) i)

化简

(2 \cdot 5 x - (- 1) \cdot 6) + (2 \cdot 6 - 1 \cdot 5 x) i : (10 x + 6) + (12 - 5 x) i

= - i x ((10 x + 6) + (12 - 5 x) i)

展开

- i x ((10 x + 6) + (12 - 5 x) i) : - 10 x^{2} i - 6 x i + 12 x - 5 x^{2}

= - 10 x^{2} i - 6 x i + 12 x - 5 x^{2}

Rewrite in standard complex form:

(12 x - 5 x^{2}) + (- 10 x^{2} - 6 x) i

= (12 x - 5 x^{2}) + (- 10 x^{2} - 6 x) i

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

e x p an d 3 (5 + 13)

s im pl i f y (8 x - 3) (6 x + 2)

e x p an d - \frac{8 x}{( x ^{2} + 1 ) ^{2}}

e x p an d \frac{cos ( 3 x ) - 16 sin ( 3 x )}{( cos ( 3 x ) ) ^{2}}