Square root of -1.....

lurflurf

Is this a joke(there was a ;))? The symbol used to represent something is not important. The "i" in Ohm's law has nothing to do with complex numbers. To avoid confusion scientist and engineers commonly use j^2=-1 when confusion might arise with another symbol, such as when i is being used to represent current.

meckano

I've read somewhere that the square root of -1 is handy when it is divided by itself, leaving ofcourse, 1.
I think it was used to show that a ?muon? leaves the opposite side of a mountain as soon as it enters the mountain.

I prefer, at times, to see the square root of -1 and division by zero as meaning that it has left our 'real' world / ceases to exist... whatever.
In the muon case above, I would see it as leaving 'reality' as it hit the mountain, and another was created at the same time on the opposite side.
Similarly, an electron in a copper conductor does not flow, rather it bumps one which bumps the next. ~~~And the little one said, roll-over, roll-over...
- solong as that is still the believed scenario for an electron.

ChrisHarvey

I've just started reading "Visual Complex Analysis" by Tristan Needham. It is an amazing book that explains complex numbers in such an clear way from a geometric point of view. I covered complex numbers in a basic way in high school and was left asking myself the same questions being asked here. What exactly are they? What do they mean? They just seemed to be a mathematical curiosity. Having only just read the first few chapters I can honestly say I feel 'happy' with them and am seeing uses for them where I woudn't usually think of them. I would recommend the book to anyone. One thing that sticks in my mind so far is the geometric derivation of Euler's formula in chapter 1. Who would have thought that e^(i*theta) = cos(theta) + i*sin(theta) could seem obvious when thought of through the eyes of geometry (and when shown!)?

Visual Complex Analysis