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 .
