square root of 0 undefined?? I was recently told that the square root of 0 is undefined because the limit of a square root didn't exist at 0. The reason is that from the negative direction you have i and from the positive direction you don't. At first, i agreed with this. It made enough sense. Then, about 5 seconds after i was out of the room, I pictured it on a complexe graph (you know, y axis = imaginary, x axis = real) and noticed that the two points were getting closer together. You could in fact say that .5i is closer to .5 than 1i is to 1. So, the limit does converge to 0 + 0i. ..right?