Subject: The number i is imaginary.
Author:
Posted on: 2014-08-13 13:33:00 UTC
It represents the square root of -1.
Now, this might not seem like something we need, but it's actually critical when doing certain calculations. Consider Euler's equation:
eix = cos(x) + i*sin(x)
notice that you obtain an imaginary component when sin(x) =/= 0.
Interestingly, adding 1 to both sides of the equation and setting x = pi gives us this result:
ei*pi+ 1 = cos(pi) + i*sin(pi) + 1
= -1 + 0 + 1
= 0
And the remarkable equation
ei*pi+ 1 = 0
Beautiful, isn't it?