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On Tue, 23 May 2023 at 06:51, Paul Royik <distan...@gmail.com> wrote:
>
> How do I simplify the following expressions: i**(-2*i), (-i)**(-2*i), ((-sqrt(3) - i)/2)**(-2*i), ((sqrt(3) - i)/2)**(-2*i) ?
>
> Is there any built-in function?
>
> For example, i**(-2*i) should give e^pi and ((sqrt(3) - i)/2)**(-2*i) should give e^(-pi/3).
The word "simplify" is ambiguous but I assume from your examples that
what you want is to rewrite powers as exponentials if possible. If so
that can be done with e.rewrite(exp):
>>> from sympy import *
>>> i = I
>>> a = i**(-2*i), (-i)**(-2*i), ((-sqrt(3) - i)/2)**(-2*i), ((sqrt(3) - i)/2)**(-2*i)
>>> [ai.rewrite(exp) for ai in a]
[exp(pi), exp(-pi), exp(-5*pi/3), exp(-pi/3)]
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Oscar
Le mardi 23 mai 2023 à 21:26:20 UTC+2, asme…@gmail.com a écrit :
On Tue, May 23, 2023 at 7:21 AM Oscar Benjamin <oscar.j....@gmail.com> wrote:On Tue, 23 May 2023 at 06:51, Paul Royik <distan...@gmail.com> wrote:
>
> How do I simplify the following expressions: i**(-2*i), (-i)**(-2*i), ((-sqrt(3) - i)/2)**(-2*i), ((sqrt(3) - i)/2)**(-2*i) ?
>
> Is there any built-in function?
>
> For example, i**(-2*i) should give e^pi and ((sqrt(3) - i)/2)**(-2*i) should give e^(-pi/3).
The word "simplify" is ambiguous but I assume from your examples thatIn this case, there's a fairly unambiguous meaning for 'simplify'. The expressions are all real, so they should be reexpressed without using i.
Oh yeah ? Wait…