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$f(z)=z$

complex_plot(x, (-4, 4), (-3, 3), aspect_ratio=1)

$f(z)=z^2$

complex_plot(x^2, (-4, 4), (-3, 3), aspect_ratio=1)

$f(z)=z^3$

complex_plot(x^3, (-4, 4), (-3, 3), aspect_ratio=1)

$f(z)=\dfrac{1}{z}$

complex_plot(1/x, (-4, 4), (-3, 3), aspect_ratio=1)

$f(z)=\dfrac{1}{z^2}$

complex_plot(1/x^2, (-4, 4), (-3, 3), aspect_ratio=1)

$f(z)=\dfrac{1}{z^3}$

complex_plot(1/x^3, (-4, 4), (-3, 3), aspect_ratio=1)