[Maxima] complex number arithmetic
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
> might be inaccurate.
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