Sure, but the question is:
is there a simple process to realize that sin(atan(37/55)/3)=1/sqrt(26)
and cos(atan(37/55)/3)=5/sqrt(26)?
Can that process be implemented in Maxima?
Cheers,
Jaime
On 02-10-2013 10:13, Aleksas Domarkas wrote:
> Example. Find all three cube roots of the complex number 110+74i.
>
> (%i1) eq:z^3=polarform(74*%i+110);
> (%o1) z^3=26^(3/2)*%e^(%i*atan(37/55))
> (%i2) T1:sin(atan(37/55)/3)=1/sqrt(26)$
> (%i3) T2:cos(atan(37/55)/3)=5/sqrt(26)$
> (%i4) solve(eq,z);
> (%o4)
> [z=((sqrt(3)*sqrt(26)*%i-sqrt(26))*%e^((%i*atan(37/55))/3))/2,
> z=-((sqrt(3)*sqrt(26)*%i+sqrt(26))*%e^((%i*atan(37/55))/3))/2,
> z=sqrt(26)*%e^((%i*atan(37/55))/3)]
> (%i5) rectform(%)$
> (%i6) subst([T1,T2],%),radcan,rectform;
> (%o6)
> [z=((5*sqrt(3)-1)*%i)/2+(-sqrt(3)-5)/2,z=-((5*sqrt(3)+1)*%i)/2-(5-sqrt(3))/2,z=%i+5]
> best
> Aleksas D
>