What is e^{(-1+i)x} ?

The solution to e^{(-1+i)x} is e^{-x}cos(x)+ie^{-x}sin(x)

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simplify e^{(-1+i)x}

simplify

e^{(- 1 + i) x}

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

Solution steps

e^{(- 1 + i) x}

Apply imaginary number rule:

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

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

Rewrite

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

in standard complex form:

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

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

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