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受欢迎的代数 >

化简 e^{it}(-i+1)

解答

化简

e^{i t} (- i + 1)

解答

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

求解步骤

e^{i t} (- i + 1)

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

= (1 - i) (cos (t) + i sin (t))

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 = 1, d = - 1

= (cos (t) \cdot 1 - sin (t) (- 1)) + (cos (t) (- 1) + sin (t) \cdot 1) i

化简

cos (t) \cdot 1 - sin (t) (- 1) : cos (t) + sin (t)

化简

cos (t) (- 1) + sin (t) \cdot 1 : - cos (t) + sin (t)

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

去除括号:

(a) = a

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

将

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

改写成标准复数形式:

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

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

流行的例子

展开 (y'(t))/((m(t)-y)(y-m(t)))

e x p an d \frac{y ^{'} ( t )}{( m ( t ) - y ) ( y - m ( t ) )}

展开 5(2xy^2+2y derivative of (yx^2))

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

展开 r(2,2,-1)*s(1,-2,3)

e x p an d r (2, 2, - 1) \cdot s (1, - 2, 3)

展开 ln(sqrt(7x^2))

e x p an d ln (7 x^{2})

展开 (((λ-1)(4λ-3)))/4

e x p an d \frac{( ( λ - 1 ) ( 4 λ - 3 ) )}{4}