# Plotting the image of a curve under a complex polynomial using Mathematica

I would be able to plot the image of a curve (say the circle with radius $1$ centered at $1+i$) under a complex polynomial (say $p(z)=z^2$) using Mathematica. I know how to find the level curves of $p$, but going the other direction I cannot figure out.

## migrated from math.stackexchange.comMay 17 '15 at 3:11

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p[z_] = z^2 + z;

• For OP's particular example, ParametricPlot[Through[{Re, Im}[(1 + I + Exp[I t])^2], {t, 0, 2 π}]. For newer versions, apparently the function ReIm[] can be used instead. – J. M. is away May 17 '15 at 4:15