> The imaginary number 'i' is sqrt(-1)... what does that even mean? Relating to phase is also hard for some people, so I try to keep it even simpler. In the s

> The imaginary number 'i' is sqrt(-1)... what does that even mean? Relating to phase is also hard for some people, so I try to keep it even simpler. In the same way that negative numbers provide directionality on a line, the complex numbers give directionality in rotation about the plane. The unit `i` is a counter-clockwise quarter-turn about the plane. -1 is a half-turn. -i is a a quarter-turn clockwise (or 3/4 turn counter-clockwise). `exp(i * tau) = 1` or `exp(i * pi) = -1` are now simple identities, referring to the fact that a full turn doesn't change orientation, and a half-turn inverts it.