zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

化简 e^{it}(e^{2it}-e^{it}+2)

解答

化简

e^{i t} (e^{2 i t} - e^{i t} + 2)

解答

(cos (t) cos (2 t) - cos^{2} (t) + 2 cos (t) - sin (t) sin (2 t) + sin^{2} (t)) + i (- sin (2 t) + sin (3 t) + 2 sin (t))

求解步骤

e^{i t} (e^{2 i t} - e^{i t} + 2)

e^{i t} = cos (t) + i sin (t)

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

使用虚数运算法则:

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

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

使用虚数运算法则:

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

= (cos (t) + i sin (t)) (cos (2 t) + i sin (2 t) - (cos (t) + i sin (t)) + 2)

使用复数算数法则:

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

a = cos (t), b = sin (t), c = cos (2 t) - cos (t) + 2, d = sin (2 t) - sin (t)

= (cos (t) (cos (2 t) - cos (t) + 2) - sin (t) (sin (2 t) - sin (t))) + (cos (t) (sin (2 t) - sin (t)) + sin (t) (cos (2 t) - cos (t) + 2)) i

化简

cos (t) (sin (2 t) - sin (t)) + sin (t) (cos (2 t) - cos (t) + 2) : - sin (2 t) + 2 sin (t) + sin (3 t)

= (cos (t) (cos (2 t) - cos (t) + 2) - sin (t) (sin (2 t) - sin (t))) + (- sin (2 t) + 2 sin (t) + sin (3 t)) i

去除括号:

(a) = a

= cos (t) (cos (2 t) - cos (t) + 2) - sin (t) (sin (2 t) - sin (t)) + (- sin (2 t) + 2 sin (t) + sin (3 t)) i

将

cos (t) (cos (2 t) - cos (t) + 2) - sin (t) (sin (2 t) - sin (t)) + (- sin (2 t) + 2 sin (t) + sin (3 t)) i

改写成标准复数形式:

(cos (t) cos (2 t) - cos^{2} (t) + 2 cos (t) - sin (t) sin (2 t) + sin^{2} (t)) + (- sin (2 t) + 2 sin (t) + sin (3 t)) i

= (cos (t) cos (2 t) - cos^{2} (t) + 2 cos (t) - sin (t) sin (2 t) + sin^{2} (t)) + (- sin (2 t) + 2 sin (t) + sin (3 t)) i

流行的例子

展开 (m^4-3m^2+1)dm

e x p an d (m^{4} - 3 m^{2} + 1) d m

展开 3(x^2-ln(2x))^2(2x-1/x)

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

展开 (3(2-z)^2)/2

e x p an d \frac{3 ( 2 - z ) ^{2}}{2}

展开 (-1,2)y(4,-2)

e x p an d (- 1, 2) y (4, - 2)

展开 (1+sin^2(x))dx

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