>>12505693It's because of shitty notation.
We're not raising something to a power, like how we do 2^5 = 2 * 2 * 2 * 2 * 2.
It's better to write it down as exp(i?) + 1 = 0.
If you use the definition of exp as (exp(x))' = exp(x) and exp(0) = 1, and generalize it to the complex numbers you'll get (exp(ix))' = (ix)' exp(ix) = i exp(x)
Since multiplying by i is just clockwise rotation by 90 degrees, we have that the derivative (velocity) of exp is always perpendicular to the position and pointing to the left.
Since:
* the velocity is always perpendicular to the position
* the velocity has length equal to the position's length
* we start at 1+0i (meaning that initial velocity is 1)
we have that the length velocity is always 1, it's always perpendicular to the left of the position, and we start from 1+0i.
So, you're just tracing the circle. If you trace it by ? (i.e. half the circle, clockwise), you'll end up at (-1+0i)
