x, y, z = symbols("x y z")
f = 1 / z**2
f_cart = f.subs(z, x + I * y)
r, i = re(f_cart), im(f_cart)
n1, n2 = 30, 30
p = plot_parametric_region(r, i, (x, -2, 2), (y, -2, 2),
    rkw_u={"color": "r", "linewidth": 0.75},
    rkw_v={"color": "b", "linewidth": 0.75},
    n1=20, n2=20, aspect="equal", xlim=(-2, 2), ylim=(-2, 2),
    xlabel="Re", ylabel="Im", title="$f(z)=%s$" % latex(f))