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

e^{av^{2}-itw}

on the form:

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

Where T = (2{\hbar}a/m)t and 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