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In addition to the solutions provided in other answers and comments, you can keep symbolic expresions, but first converting them with the help of the fast_callable function, that is:

xuv = fast_callable(sqrt(u + I*v).real(), vars=[u,v])
yuv = fast_callable(sqrt(u + I*v).imag(), vars=[u,v])
zuv = v
parametric_plot3d([xuv, yuv, zuv], (u,-1,1), (v,-1,1))