化简 2i(cos(x)+isin(x))(2-cos(x)+isin(x))^2

解答

化简

2 i (cos (x) + i sin (x)) (2 - cos (x) + i sin (x))^{2}

- 6 sin (x) + (8 cos (x) + 2 cos (- x) - 8 cos^{2} (x) - 8 sin^{2} (x)) i

求解步骤

2 i (cos (x) + i sin (x)) (2 - cos (x) + i sin (x))^{2}

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

使用分配律:

a (b + c) = ab + a c

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

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

化简

2 i (2 - cos (x) + i sin (x))^{2} cos (x) + 2 i (2 - cos (x) + i sin (x))^{2} i sin (x) : i (8 cos (x) + 2 cos (- x) - 8 cos^{2} (x) - 8 sin^{2} (x)) - 6 sin (x)

= i (8 cos (x) + 2 cos (- x) - 8 cos^{2} (x) - 8 sin^{2} (x)) - 6 sin (x)

展开

i (8 cos (x) + 2 cos (- x) - 8 cos^{2} (x) - 8 sin^{2} (x)) : 8 cos (x) i + 2 cos (- x) i - 8 cos^{2} (x) i - 8 sin^{2} (x) i

= 8 cos (x) i + 2 cos (- x) i - 8 cos^{2} (x) i - 8 sin^{2} (x) i - 6 sin (x)

Rewrite in standard complex form:

- 6 sin (x) + (8 cos (x) + 2 cos (- x) - 8 cos^{2} (x) - 8 sin^{2} (x)) i

= - 6 sin (x) + (8 cos (x) + 2 cos (- x) - 8 cos^{2} (x) - 8 sin^{2} (x)) i

e x p an d \frac{x ^{5}}{( x ^{2} + 4 ) ^{3}}

e x p an d (1 + 2 e)^{3}

e x p an d x (y = 2 y + x)

s im pl i f y 2 x \cdot (- \frac{1}{x ^{2}} + 4)

e x p an d (5 x^{2} + 2 x + 1)^{3} + ln (x + 1)