On Oct 21, 2008, A. Valverde wrote:
>what is wrong with the following: to the input
>solve(z*conjugate(z)+3*(z-conjugate(z))=13+12*%i, z)
>Maxima give sqrt(13+12*%i) as solution, but it is not correct!
>
There are probably ways to work directly with complex numbers
in a solve(...) problem, but
I have not learned them yet.
Here is a work-around at least:
We need to get Maxima (ie solve(...) ) to recognise
that we are supplying two equations to solve for
the two unknowns (z and zbar, or x and y).
==============
(%i1) display2d : false$
(%i2) eq : z*zb + 3*(z - zb) = 13 + 12*%i;
(%o2) z*zb + 3*(z - zb) = 12*%i + 13
(%i3) [z : x + %i*y, zb : conjugate(z) ];
(%o3) [ %i*y + x, x - %i*y ]
(%i4) eq1 : realpart ( ev( eq ) );
(%o4) y^2 + x^2 = 13
(%i5) eq2 : imagpart ( ev( eq) );
(%o5) 6*y = 12
(%i6) s : solve ( [ eq1, eq2 ] , [ x , y ] );
(%o6) [ [ x = 3, y = 2] , [ x = -3, y = 2 ] ]
(%i7) zsoln : makelist( subst( s[j], zv = x + %i*y ), j, 1, length(s) );
(%o7) [ zv = 2*%i + 3, zv = 2*%i - 3 ]
For what it's worth,
Ted Woollett