
theorem Th24:
  for a being Complex st a <> 0 holds cos Arg a = Re a / |.
  a.| & sin Arg a = Im a / |.a.|
proof
  let a be Complex;
  a = |.a.|*cos Arg a+(|.a.|*sin Arg a)*<i> by COMPTRIG:62;
  then
A1: Re a = |.a.|*cos Arg a & Im a = |.a.|*sin Arg a by COMPLEX1:12;
  assume a <> 0;
  hence thesis by A1,COMPLEX1:45,XCMPLX_1:89;
end;
