What is simplify-3/13 e^{(-2+3i)t} ?

The solution to simplify-3/13 e^{(-2+3i)t} is -(3e^{-2t}cos(3t))/(13)-i(3e^{-2t}sin(3t))/(13)

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simplify-3/13 e^{(-2+3i)t}

simplify

- \frac{3}{13} e^{(- 2 + 3 i) t}

- \frac{3 e ^{- 2 t} cos ( 3 t )}{13} - i \frac{3 e ^{- 2 t} sin ( 3 t )}{13}

Solution steps

- \frac{3}{13} e^{(- 2 + 3 i) t}

e^{(- 2 + 3 i) t} = e^{- 2 t} (cos (3 t) + i sin (3 t))

= - \frac{3}{13} e^{- 2 t} (cos (3 t) + i sin (3 t))

Rewrite

- \frac{3}{13} e^{- 2 t} (cos (3 t) + sin (3 t) i)

in standard complex form:

- \frac{3 e ^{- 2 t} cos ( 3 t )}{13} - \frac{3 e ^{- 2 t} sin ( 3 t )}{13} i

= - \frac{3 e ^{- 2 t} cos ( 3 t )}{13} - \frac{3 e ^{- 2 t} sin ( 3 t )}{13} i

(9 x^{2} + y - 1) d x - (4 y - x) d y

- 3 (- 2 x)^{2} + 5 (- 2 x)

\frac{2 x ^{3} - 1}{( x ^{3} + 1 ) ^{2}}

\frac{14}{3 ( 2 s + 3 )}

\frac{( - 3 - x ) ^{2}}{2}

What is simplify-3/13 e^{(-2+3i)t} ?
The solution to simplify-3/13 e^{(-2+3i)t} is -(3e^{-2t}cos(3t))/(13)-i(3e^{-2t}sin(3t))/(13)