I think Jaime Villate's solution so far is the simplest:
float(rectform(solve(z^3=110+74*%i,z)));
The polar form for 110*74i is 26^(3/2)*exp(i*arctan(37/55)) of which the
"principal" cube root, using de Moivre's theorem, would be
26^(1/2)*exp(i*arctan(37/55)/3).
I'm not quite sure what machinations are required to obtain the rectangular
form of this analytically without using "float"; I suspect there is no easy
method.
On Tue, Oct 1, 2013 at 8:46 PM, Aleksas Domarkas <aleksasd873 at gmail.com>wrote:
> see
> http://www.math.utexas.edu/pipermail/maxima/2013/034120.html
>
> The cube root of 110+74i would return 5+i.
> How compute this?
>
> (%i1) expand((5+%i)^3);
> (%o1) 74*%i+110
>
> Aleksas D
>
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