On Tue, Apr 29, 2008 at 1:44 PM, Jean-Pierre Gerbal <
jean-pierre.gerbal at ac-orleans-tours.fr> wrote:
> is there a way(*) to solve a complex equation with conjugate as :
>
> solve([conjugate(z)-3*%i*z-3+6*%i=0], [z]);
>
Maxima assumes that variables are real-valued by default (even with
domain:complex), so conjugate(z) will yield z. This can be solved by
declare(z,complex).
But alas, Maxima's solve command knows nothing about "conjugate", so this
doesn't help with the original problem.
The easiest way to solve it is to explicitly solve for the real and
imaginary parts:
z:a+%i*b$
conjugate(z)-3*%i*z-3+6*%i => -3*%i*(%i*b+a)-%i*b+a+6*%i-3
[realpart(%),imagpart(%)] => [3*b+a-3,-b-3*a+6]
solve(%,[a,b]) => [[a = 15/8,b = 3/8]]
subst(%[1],z) => 3*%i/8+15/8
-s