Contour plots over the complex plane

Real and imaginary parts over the complex plane

Contour plot of the real part (red) and imaginary part (blue) of over the . Here . By the Cauchy–Riemann equations, the curves of constant real part and constant imaginary part are orthogonal. The curves of constant real part are circles and the curves of constant imaginary part are rays.

Curves of vanishing real part (red) and imaginary part (blue) of over the . Here .

Absolute value and argument over the complex plane

Contour plot of the absolute value (violet) and argument (green) of over the . Here .

Real and imaginary parts over the complex plane around infinity

Contour plot of the real part (red) and imaginary part (blue) of over the . Here .

Curves of vanishing real part (red) and imaginary part (blue) of over the . Here .

Absolute value and argument over the complex plane around infinity

Contour plot of the absolute value (violet) and argument (green) of over the . Here .