Complex numbers written in exponential form.

z^4 = 81*e^(Pi/2)i

I have no idea how to find the roots for this equation. Can someone talk me through the algebra?

z^4 = 81*e^(Pi/2)i
z^4 = 81*e^((Pi/2)+2Kpi)i  (since you go round in a circle, provided k is an integer)
z = (81*e^((Pi/2)+2Kpi)i)^.25  (fourth root each side)
z = (81^.25)*e^(((pi/2)+2Kpi)i/4) (by laws of indicies, you can split and multiply the two exponents)
z=3*e^(((4k+1)pi)/8)i (rearrange)
z=3*e^(pi/8)i (k=0)
z=3*e^(5pi/8)i (k=1)
z=3*e^(11pi/8)i (k=2)
z=3*e^(15pi/8)i (k=3)
then cos+isin those angles to get them in cartesian form.