# [Maxima] complex number arithmetic

Richard Fateman fateman at cs.berkeley.edu
Thu Apr 16 16:56:52 CDT 2009

```You need to choose a principal value for multiple-valued roots.
Also try rectform((1+%i)^(1+%i)) for a fun time.

Barton Willis wrote:
>> What about complex exponentiation?  Probably the most user-friendly
>> rule would be that we would do it whenever the result is correctly
>> expressed in numbers only.  The easy case is integral powers:
>>
>>       (1+2*%i)^3 => -2*%i-11
>>       1/(1+%i) => 1/2 - %i/2   (though arguably (1-%i)/2 is clearer in
>> some contexts)
>>
>
> With large integer powers, maybe it's not clear what is best. Computations
> such as
>
>
>> a : (2/3 + %i)^(10^9 + 1);
>> b : (2/3 + %i)^(10^9);
>> a/b  --> (long number) / (long number) --> 2/3 + %i
>>
>
> are somewhat embarrassing. And for complex floating point, such
> computations
> might be inaccurate.
>
> Barton
>
>
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```