Solving the Mystery of i & j: The Square Root of -1

[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