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.

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 the imaginary part (blue) of over the . Here . The essential singularity at results in a complicated structure of the contour lines.

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 . The essential singularity at results in a complicated structure of the contour lines.