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Popular >

simplify (e^{ix}-e^{-ix})^2

Solution

simplify

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

Solution

- 4 sin^{2} (x)

Solution steps

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

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

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

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

Expand

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

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

Apply exponent rule:

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

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

2^{2} = 4

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

i^{2} = - 1

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

Refine

= - 4 sin^{2} (x)

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Frequently Asked Questions (FAQ)

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