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

theorem Th32:
  (z1 + z2)*' = z1*' + z2*'
proof
  thus Re ((z1 + z2)*') = Re(z1 + z2) by Th27
    .= Re z1 + Re z2 by Th8
    .= Re (z1*') + Re z2 by Th27
    .= Re (z1*') + Re (z2*') by Th27
    .= Re (z1*'+ z2*') by Th8;
  thus Im ((z1 + z2)*') = -Im(z1 + z2) by Th27
    .= -(Im z1 + --Im z2) by Th8
    .= -Im z1 + -Im z2
    .= Im (z1*') + -Im z2 by Th27
    .= Im (z1*') + Im (z2*') by Th27
    .= Im (z1*' + z2*') by Th8;
end;
