Hi. Consider the real and imaginary parts of your gamma(t).

Re[Gamma(t)] = 2 + 3*Cos[t]

Im[Gamma(t)] = 3*Sin[t] - 1

So on the real/imaginary plane, your real (x) coordinate is given by:

2 + 3*Cos[t]

and your imaginary (y) coordinate is given by:

3*Sin[t] - 1

This will give a circle of radius 3 with center at (2,-1) that is 2*Pi periodic. Plug in t = 0 and it will give you your starting and ending point (ending being at t = 2*Pi) since they are the same point.

For the second part, it is transforming your gamma into something else. Put in your gamma for z and multiply it out and then once again separate the real and imaginary parts and you will have your x(t) and y(t).

As far as standard parametrization, I'm not sure what that is.