unit complex;

interface

type
  tcomplex = record
    re, im: real;
  end;

function  AbsComplex(z: tcomplex): real;

procedure AddComplex(z1, z2: tcomplex; var res: tcomplex);
procedure SubComplex(a, b: tcomplex; var res: tcomplex);

procedure ScaleComplex(var z: tcomplex; c: real);
procedure MultComplex(z1, z2: tcomplex; var res: tcomplex);
function  DivComplex(a, b: tcomplex; var res: tcomplex): boolean;
procedure PowerComplex(z: tcomplex; var res: tcomplex; n: integer);

procedure PrintComplex(z: tcomplex);


implementation

function AbsComplex(z: tcomplex): real;
begin
  AbsComplex := sqrt(sqr(z.re) + sqr(z. im))
end;

procedure AddComplex(z1, z2: tcomplex; var res: tcomplex);
begin
  res.re := z1.re + z2.re;
  res.im := z1.im + z2.im;
end;

procedure SubComplex(a, b: tcomplex; var res: tcomplex);
begin
  res.re := a.re - b.re;
  res.im := a.im - b.im;
end;

procedure MultComplex(z1, z2: tcomplex; var res: tcomplex);
begin
  res.re := z1.re * z2.re - z1.im * z2.im;
  res.im := z1.re * z2.im + z1.im * z2.re
end;

procedure ScaleComplex(var z: tcomplex; c: real);
begin
  z.re := z.re * c;
  z.im := z.im * c
end;

function DivComplex(a, b: tcomplex; var res: tcomplex): boolean;
begin
  DivComplex := false; // False = error / True = Ok
  if (b.re = 0) and (b.im = 0) then exit
  else begin
    res.re := ((a.re*b.re)+(a.im*b.im))/((b.re*b.re)+(b.im*b.im));
    res.im := ((a.im*b.re)-(a.re*b.im))/((b.re*b.re)+(b.im*b.im));
  end;
end;


procedure PowerComplex(z: tcomplex; var res: tcomplex; n: integer);
var
  i: integer;
  T: tcomplex;
begin
  T := z;
  for i := 2 to n do begin
    MultComplex(T, z, T);
  end;
  res := T;
end;


procedure PrintComplex(z: tcomplex);
const
  sign: array[boolean] of char = ('-', '+');
begin
  write(z.re:6:1, sign[z.im > 0], abs(z.im):6:1, '*i');
end;


end.