Complex potential of a metallic cylinder

[xago]

Homework Statement

Construct a complex potential in the w-plane which corresponds to a charged metallic cylinder of unit radius having a potential Vo on its surface.

The Attempt at a Solution

I'm a bit confused on how to start deriving a complex potential for the cylinder. If I was given the charge of the cylinder I know i could use Gauss's Law to find the electric field and derive that to get the potential. However I'm not sure how to deal with unit circle with a constant potential on the surface. The 2D plane for the cylinder just gives a unit circle and the w-plane is just u on the x-axis and v on the y-axis (w = u + iv)
This problem is from a math course and I'm a bit rusty on my electrostatics

 

[xago]

Should I just assume a charge per unit length of Q on the cylinder, use gauss law to get the electric then derive that to get the potential which I simply add Vo to?