negative base raised to fractional exponent

Steve Holden steve at holdenweb.com
Wed Oct 17 00:03:24 CEST 2007


schaefer.mp at gmail.com wrote:
> Does anyone know of an approximation to raising a negative base to a
> fractional exponent? For example, (-3)^-4.11111 since this cannot be
> computed without using imaginary numbers. Any help is appreciated.
> 
A couple of questions.

1. How do you approximate a complex number in the reals? That doesn't 
make sense.

2. x ^ -4.1111 = 1 / (x ^ 4.1111), so where do complex numbers enter 
into this anyway?

3. I think you will find the complex numbers start to emerge as you 
explore fractional exponents.

This being Python, and an interactive interpreter being available, you 
can always just try it:

 >>> -3 ** -4.1111
-0.010927147607830808
 >>> -1 ** -2
-1.0
 >>> (-1+0j) ** (-2)
(1+0j)
 >>> (-1+0j) ** (0.5)
(6.123233995736766e-17+1j)
 >>> (-3 + 0j) ** (-4.1111 + 0j)
(0.010268290423601775-0.0037369461622949107j)
 >>>

regards
  Steve
-- 
Steve Holden        +1 571 484 6266   +1 800 494 3119
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