en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (e^{3xi}-e^{-3xi})^2

Solution

simplify

(e^{3 x i} - e^{- 3 x i})^{2}

Solution

- 4 sin^{2} (3 x)

Solution steps

(e^{3 x i} - e^{- 3 x i})^{2}

e^{3 x i} = cos (3 x) + i sin (3 x)

e^{- 3 x i} = cos (3 x) - i sin (3 x)

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

Expand

cos (3 x) + sin (3 x) i - (cos (3 x) - i sin (3 x)) : 2 i sin (3 x)

= (2 i sin (3 x))^{2}

Apply exponent rule:

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

= 2^{2} i^{2} sin^{2} (3 x)

2^{2} = 4

= 4 i^{2} sin^{2} (3 x)

i^{2} = - 1

= 4 (- 1) sin^{2} (3 x)

Refine

= - 4 sin^{2} (3 x)

Popular Examples

expand (9,4)y(-3,-2)expand

(9, 4) y (- 3, - 2)

expand x/((1+x)sin(2x))expand

\frac{x}{( 1 + x ) sin ( 2 x )}

expand ((4-(u-2)^2))/u*(u-2)expand

\frac{( 4 - ( u - 2 ) ^{2} )}{u} \cdot (u - 2)

expand-(2(4e^{pi/2}+4))/pi expand

- \frac{2 ( 4 e ^{\frac{π}{2}} + 4 )}{π}

expand-{-5+3x^3-[-(6/3+2)]}expand

- {- 5 + 3 x^{3} - [- (\frac{6}{3} + 2)]}

Frequently Asked Questions (FAQ)

What is (e^{3xi}-e^{-3xi})^2 ?
The solution to (e^{3xi}-e^{-3xi})^2 is -4sin^2(3x)