I would like to show how I can rewrite the function:

$\displaystyle e^{av^{2}-itw}$

on the form:

$\displaystyle e^{av^{2}/(1+iT)}/(\sqrt{1+iT})$

Where $\displaystyle T = (2{\hbar}a/m)t$ and $\displaystyle v=((L/2a)+iu)$



I guess there are some formulas concerning exponentials/complex numers I have to use in order to solve this problem. However, I can't seem to figure out which ones