Show that
$\displaystyle \frac{d^n}{dx^n} (e^{ax}sinbx) = r^ne^{ax}sin(bx+n\theta) $
where $\displaystyle a$ and $\displaystyle b$ are positive numbers, $\displaystyle r^2 = a^2 + b^2$ and $\displaystyle \theta =tan^{-1}(b/a)$
Complex numbers are very useful. They also have some interesting properties. One is, if:
$\displaystyle
z = r ( cos (\theta) + i sin (\theta) )
$
then
$\displaystyle
z^n = r^n ( cos (n\theta) + i sin (n\theta) )
$
Check your text for a review on complex numbers.