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On the real axis The function  along the real axis.  is real‐valued in for  . At  , the function  has a square root branch point. The function  along the real axis. The left graphic shows  and the right graphic shows  . The absolute value and the argument of  along the real axis. The left graphic shows  and the right graphic shows  . The argument is piecewise constant for  . On the real axis at infinity The function  along the real axis. The left graphic shows  and the right graphic shows  . The imaginary part is piecewise constant on the real axis. At  , the function  has a logarithmic singularity. The absolute value and the argument of  along the imaginary axis. The left graphic shows  and the right graphic shows  . The argument is constant for  . On the imaginary axes The real part and the imaginary part of  along the imaginary axis. The left graphic shows  and the right graphic shows  . Along the imaginary axis, the imaginary part is piecewise constant. The absolute value and the argument of  along the imaginary axis. The left graphic shows  and the right graphic shows  . On the imaginary axis at infinity The function  along the imaginary axis. The left graphic shows  and the right graphic shows  . The absolute value and the argument of  along the imaginary axis. The left graphic shows  and the right graphic shows  . On the unit circle The real part and the imaginary part of  on the unit circle. The left graphic shows  and the right graphic shows  . The absolute value and the argument of  on the unit circle. The left graphic shows  and the right graphic shows  .
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