What is ie^{(-2+i100)t} ?

The solution to ie^{(-2+i100)t} is -e^{-2t}sin(100t)+ie^{-2t}cos(100t)

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simplify ie^{(-2+i100)t}

simplify

i e^{(- 2 + i 100) t}

- e^{- 2 t} sin (100 t) + i e^{- 2 t} cos (100 t)

Solution steps

i e^{(- 2 + i 100) t}

e^{(- 2 + i 100) t} = e^{- 2 t} (cos (100 t) + i sin (100 t))

= i e^{- 2 t} (cos (100 t) + i sin (100 t))

Apply complex arithmetic rule:

(ai) (b + c i) = - a c + abi

a = e^{- 2 t}, b = cos (100 t), c = sin (100 t)

= - e^{- 2 t} sin (100 t) + e^{- 2 t} cos (100 t) i

(\frac{3 x - 3}{2}) \cdot (\frac{x - 1}{3})

e^{x} sin (3 x) - e^{x} cos (3 x) (D^{2} - 2 D + 10)

, (- 3 + 8 i) (6 + 2 i)

7 (- 9 - 715)

\frac{2000 s - 2000 e ^{- s}}{s ^{2} ( s ^{2} + 200 s + 200 )}

What is ie^{(-2+i100)t} ?
The solution to ie^{(-2+i100)t} is -e^{-2t}sin(100t)+ie^{-2t}cos(100t)