Complex equation

No, setting domain to complex isn't enough. To prevent conjugate(z)
from simplifying to z, declare z complex; for example

(%i1) declare(z,complex)$
(%i4) eq : conjugate(z)-3*%i*z-3+6*%i=0;
(%o4) conjugate(z)-3*%i*z+6*%i-3=0
(%i5) [eq, conjugate(eq)];
(%o5) [conjugate(z)-3*%i*z+6*%i-3=0,3*%i*conjugate(z)+z-6*%i-3=0]

I'm more comfortable doing conjugate(z) --> zb:

(%i6) subst(conjugate(z) = zb,%);
(%o6) [zb-3*%i*z+6*%i-3=0,3*%i*zb+z-6*%i-3=0]
(%i7) solve(%,[z,zb]);
(%o7) [[z=(3*%i+15)/8,zb=-(3*%i-15)/8]]

Barton

maxima-bounces at math.utexas.edu wrote on 04/29/2008 01:09:40 PM:

> >> ps : another way as to solve as linear system the real part and the
> >> imagpart of the equation
> >
> > (%i1) solve([conjugate(z)-3*%i*z-3+6*%i=0], [z]), domain:complex;
> > (%o1) [z = (6*%i-3)/(3*%i-1)]
> 
> I'm sorry, the correct answer:
> 
> (%i1) eq : conjugate(z)-3*%i*z-3+6*%i=0$
> (%i2) solve(eq,z), domain:complex;
> (%o2) [z = (6*%i-3)/(3*%i-1)]
> (%i3) at(eq,%), rectform;
> (%o3) 0 = 0
> (%i4) z : a+%i*b$
> (%i5) solve(eq, [a,b]), rectform;
> (%o5) [[a = -%i*(8*%r3-3)/10-(6*%r3-21)/10,b = %r3]]
> (%i6) at(eq,%[1]), rectform,ratexpand;
> (%o6) 0 = 0
> 
> -- 
> Alexey Beshenov <al at beshenov.ru>
> http://beshenov.ru/
> [attachment "attqw0pg.dat" deleted by Barton Willis/MATH/UNK/UNEBR] 
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