square root (idea)

But, any complex number has n nth roots, thus two square roots. Take a real number

x = x + 0*i = x * e^0*i = x * e^2*pi*i

The square roots are

x^1/2 * e^1/2*0*i = x^1/2 * 1 = x^1/2
and
x^1/2 * e^1/2*2*pi*i = x^1/2 * -1 = -x^1/2

Update 2002-11-12: The definition of a square root has disappeared! I suggest the following, simple definition:

The sqare root of a number x is a number whose square is x.

I am sure someone can node a much more mathematical definition than this.