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Popular >

simplify e^t(e^{ib}-e^{-ib})

Solution

simplify

e^{t} (e^{ib} - e^{- ib})

Solution

2 i e^{t} sin (b)

Solution steps

e^{t} (e^{ib} - e^{- ib})

e^{ib} = cos (b) + i sin (b)

e^{- ib} = cos (b) - i sin (b)

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

Expand

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

= 2 i e^{t} sin (b)

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Frequently Asked Questions (FAQ)

What is e^t(e^{ib}-e^{-ib}) ?
The solution to e^t(e^{ib}-e^{-ib}) is 2ie^tsin(b)