Re: y=sqrt(x)+2

On 2/16/25 9:27 AM, Richard Hachel wrote:

Le 16/02/2025 à 02:42, Richard Damon a écrit :

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4 * i^4

 Absolutely.
 J'avais toujours dit que les Richard étaient des êtres exceptionnels.
 Nota bene:
4 * i^4 = -4

No, i^4 - 1, since i^2 = -1, by definition.
The problem is that when we collapse to a simple Cartesian system, we lose the wraps, so non-integer powers become somewhat indeterminate and multiplicative. The "angle" of a number is only known to within a modulus of 2xPi (or 360 degrees) and thus the square root of any number has two values. When in just the real domain, we can limit to the principle limb, but once we allow for complex numbers, we lose that option.

 In Cartesian representation, point A, root of the equation f(x)=sqrt(x)+2, is located at A (-4,0) in standard coordinates, and at A(4i,0) in imaginary coordinates.
 R.H.