reserve a,b,c,d for Real;
reserve z,z1,z2 for Complex;

theorem Th35:
  (z1*z2)*' = z1*'*z2*'
proof
A1: Re(z1*') = Re z1 & Re(z2*') = Re z2 by Th27;
A2: Im(z1*') = -Im z1 & Im(z2*') = -Im z2 by Th27;
  thus Re((z1*z2)*') = Re(z1*z2) by Th27
    .= (Re (z1*') * Re (z2*')) - (-Im (z1*')) * -Im (z2*') by A1,A2,Th9
    .= (Re (z1*') * Re (z2*')) - --(Im (z1*') * Im (z2*'))
    .= Re(z1*'*z2*') by Th9;
  thus Im((z1*z2)*') = -Im(z1*z2) by Th27
    .= -((Re (z1*') * -Im (z2*')) + (Re (z2*') * -Im (z1*'))) by A1,A2,Th9
    .= (Re (z2*') * Im (z1*'))+--(Re (z1*') * Im (z2*'))
    .= Im(z1*'*z2*') by Th9;
end;
