化简 (1-e^{ix})^2

解答

化简

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

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

求解步骤

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

使用虚数运算法则:

e^{ia} = cos (a) + i sin (a)

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

乘开

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

= (1 - cos (x) - i sin (x))^{2}

s im pl i f y (x + 5 - 3) \cdot (x + 5 + 3)

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

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

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

e x p an d P (6, 2, - 5) Q (0, - 5, - 3)