化简 2(1+cos(x))e^{-ix}

解答

化简

2 (1 + cos (x)) e^{- i x}

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

求解步骤

2 (1 + cos (x)) e^{- i x}

e^{- i x} = cos (x) - i sin (x)

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

将

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

改写成标准复数形式:

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

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

e x p an d ln (x^{7} + 8)

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

e x p an d (8 x^{2} - 2 x y + 3) \frac{d x}{d y}

e x p an d - (- 2 x^{2} + 3 x - 7 = 0)

e x p an d 14 a + 18 a