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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.
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