化简 e^{ix}+e^{i(x+pi/8)}

解答

化简

e^{i x} + e^{i (x + \frac{π}{8})}

(cos (x) + cos (\frac{π + 8 x}{8})) + i (sin (\frac{π + 8 x}{8}) + sin (x))

求解步骤

e^{i x} + e^{i (x + \frac{π}{8})}

使用虚数运算法则:

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

= cos (x) + i sin (x) + e^{i (x + \frac{π}{8})}

使用虚数运算法则:

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

= cos (x) + i sin (x) + cos (\frac{8 x + π}{8}) + i sin (\frac{8 x + π}{8})

将

cos (x) + sin (x) i + cos (\frac{8 x + π}{8}) + sin (\frac{8 x + π}{8}) i

改写成标准复数形式:

(cos (x) + cos (\frac{8 x + π}{8})) + (sin (x) + sin (\frac{8 x + π}{8})) i

= (cos (x) + cos (\frac{8 x + π}{8})) + (sin (x) + sin (\frac{8 x + π}{8})) i

e x p an d \frac{3 ( 1 + 5 e ^{6 x} )}{1 - 5 e ^{6 x}}

\frac{d}{d s} ((K (s)) (s + 3))

e x p an d 3 (5 c - 4 = 8 c + 2)

e x p an d \frac{( 6 - y ) ^{3}}{3 y}

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