Simplify expressions involving complex numbers

[Paul Royik]

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).

Thank you.

[Oscar Benjamin]

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)]

--
Oscar

[Peter Stahlecker]

Your replies are the best way to learn more about sympy, thanks!!

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Peter Stahlecker

[Paul Royik]

Thank you!

[Aaron Meurer]

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 that

In this case, there's a fairly unambiguous meaning for 'simplify'. The expressions are all real, so they should be reexpressed without using i.

Aaron Meurer

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)]

--
Oscar

[emanuel.c...@gmail.com]

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 that

In 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…