This GeoGebra worksheet illustrates why the complex logarithm is not defined on the negative real axis. Notice that the argument jumps from -π to +π as you cross the negative x-axis, and the value of the logarithm also jumps. Since discontinuous functions are undesirable, it is preferable to remove the discontinuity by leaving log(z) undefined when z is a negative real number.

Instructions: Move the red point by clicking and dragging.