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Cosider the two options:

f(z)=z^2
complex_plot(f, (-3, 3), (-3, 3), plot_points=300, 
    contoured=True, tiled=True, cmap='plasma',aspect_ratio=1)

or

M = Manifold(2, 'M')                  
X.<x,y> = M.chart()                
N = Manifold(2,'N')
U.<u,v> = N.chart()
z=(x+I*y)
def f(z):
    return z^2
F = M.diff_map(N,[f(z).real(),f(z).imag()], name='F')
p1=X.plot(U,mapping=F,number_values={x:20,y:20},
      ranges={x:(-3,3),y:(-3,3)},
      color='grey',thickness=1,label_axes=False) 
p1.show(aspect_ratio=0.6)