This isn't anything fancy, but it's useful enough for me to put in a book eventually (on Geogebra). and it's actually ln(z) when Re{z}=0, and a bit more, essentially just ln(0+i), but I call it ln(0) because people get unreasonable upset, and that is somewhat amusing.
Solved for real, in several different ways, this is the only way to describe ln(0) and have it mean anything. It's essentially just where the principle logarithm intersects the imaginary (y) axis, in the positive direction. The most important thing I neglected is that ln(0) is a strictly 2 dimensional number, it just represents the initial intercept.
Ln(0) IS STILL UNDEFINED IN THE REAL PLANE. This is a way to get rid of it. Oh, and the absolute value of any ln(0) relative to any function is always the inverse square root of 2, even if it remains undefined. I swear, it's the only way to get it to work out consistently.
