.
beep
(beep <small>-iota also wanted to chime in</small>)
@shroomie @monorail With real numbers, you can't have a square root of -1 (because multiplying two numbers with the same sign always gives a positive number)
For imaginary numbers, you just posit that there is a square root of -1, and it's called i
(some applications call it j
instead)
So i * i = -1
. Now if you want a square root of e.g. -25, that's 5i
. Every number in the set of imaginary numbers has a real part and imaginary part, for example i
is just 0 + 1i
, but it's also possible to have imaginary numbers that have a real and an imaginary part, for example 3 + 5i
.
If you've ever seen the real numbers represented visually on a line, like this:[to -Infinity] <- -3 2 1 0 1 2 3 -> [to +Infinity]
then you can imagine the imaginary numbers extending that by a 2nd axis!
There are some cool applications of this stuff, but I am too bad at maths to remember any of them, maybe Holly Glaceon can explain better...