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Popular >

simplify a(e^{-ikx}-e^{ikx})

Solution

simplify

a (e^{- ik x} - e^{ik x})

Solution

- 2 ia sin (k x)

Solution steps

a (e^{- ik x} - e^{ik x})

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

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

= a (cos (k x) - i sin (k x) - (cos (k x) + i sin (k x)))

Expand

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

= a (- 2 i sin (k x))

Remove parentheses:

(- a) = - a

= - a \cdot 2 i sin (k x)

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Frequently Asked Questions (FAQ)

What is a(e^{-ikx}-e^{ikx}) ?
The solution to a(e^{-ikx}-e^{ikx}) is -2iasin(kx)