I know how to use i... and I know that complex numbers are mighty useful (I'm an electronic engineer, so I used them a lot)... and how they keep popping all over the place in physics. So I'm sure the algebra behind i works. But, it never bugged anyone here that we use something that doesn't really exist? I mean, one of the first things we learn in Logic is that from a falsehood you can derive either true statement or a false statement. So while I used i a lot, I cannot claim I can say that "i such that i2=-1" exists... just that the algebra built around it works. It's a similar thing to this: I know that there is no ρ such that ρ = 0 and ρ = 1. But if it existed, then one could find it has such-and-such very practical properties. Perhaps it could be used as a shortcut for some mathematical calculations, even though it is impossible, doesn't exist, doesn't make sense and can never be measured. I have been mighty bugged with i for the last 20 years: one because it works, and two because everybody love something that is impossible and illogical. Anyone else ever felt similarly helpless with i? That we just use it because we were told to use and it works, but if we had been left to our own devices we would never think of something as crazy?