化简 (e^{ix}-cos(x))^2

解答

化简

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

- sin^{2} (x)

求解步骤

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

使用虚数运算法则:

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

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

化简

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

= (i sin (x))^{2}

使用指数法则:

(a \cdot b)^{n} = a^{n} b^{n}

= i^{2} sin^{2} (x)

i^{2} = - 1

= - 1 \cdot sin^{2} (x)

乘以:

1 \cdot sin^{2} (x) = sin^{2} (x)

= - sin^{2} (x)

e x p an d \frac{2 x ^{3} - x + 4}{x + 1} + x^{2}

e x p an d (1 + b e) (1 + a d)

e x p an d \frac{( 5 - 2 m ^{5} ) ^{2}}{25}

e x p an d x^{2} (x^{3} + 5 x^{2} - 3 x + 3)

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