On the real axis The function along the real axis. is real‐valued along the real axis. The absolute value and the argument of along the real axis. The left graphic shows and the right graphic shows . The argument vanishes identically on the real axis. On the real axis at infinity The function along the real axis. The left graphic shows and the right graphic shows . is discontinuous at . The left‐sided limit is 0, and the right‐sided limit is . The absolute value and the argument of along the real axis. The left graphic shows and the right graphic shows . The argument vanishes identically on the real axis. 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, is real‐valued and the imaginary part vanishes identically. The absolute value and the argument of along the imaginary axis. The left graphic shows and the right graphic shows . The argument is piecewise constant. On the imaginary axis at infinity The function along the imaginary axis. The left graphic shows and the right graphic shows . At , the function has an essential singularity. 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 .
