
theorem Th10:
  for a,b be Element of F_Complex st Im a = 0 holds
  Re (a*b) = Re a * Re b & Im (a*b) = Re a * Im b
proof
  let a,b be Element of F_Complex;
  assume
A1: Im a = 0;
  hence Re (a*b) =Re a * Re b - 0 * Im b by HAHNBAN1:11
    .= Re a * Re b;
  thus Im (a*b) = Re a* Im b+ Re b * 0 by A1,HAHNBAN1:11
    .= Re a * Im b;
end;
