unit cplx;

interface

type

 PReal = ^TReal;
 TReal = extended;

 PComplex = ^TComplex;
 TComplex = record
   r: TReal;
   i: TReal;
 end;

function MakeComplex(x, y: TReal): TComplex;
function Sum(x, y: TComplex): TComplex;
function Difference(x, y: TComplex): TComplex;
function Product(x, y: TComplex): TComplex;
function TimesReal(x: TComplex; y: TReal): TComplex;
function PlusReal(x: TComplex; y: TReal): TComplex;
function EiT(t: TReal): TComplex;
function ComplexToStr(x: TComplex): string;
function AbsSquared(x: TComplex): TReal;

implementation

uses SysUtils;

function MakeComplex(x, y: TReal): TComplex;
begin
 with result do
 begin
   r := x;
   i := y;
 end;
end;

function Sum(x, y: TComplex): TComplex;
begin
 with result do
 begin
   r := x.r + y.r;
   i := x.i + y.i;
 end;
end;

function Difference(x, y: TComplex): TComplex;
begin
 with result do
 begin
   r := x.r - y.r;
   i := x.i - y.i;
 end;
end;

function EiT(t: TReal): TComplex;
begin
 with result do
 begin
   r := cos(t);
   i := sin(t);
 end;
end;

function Product(x, y: TComplex): TComplex;
begin
 with result do
 begin
   r := x.r * y.r - x.i * y.i;
   i := x.r * y.i + x.i * y.r;
 end;
end;

function TimesReal(x: TComplex; y: TReal): TComplex;
begin
 with result do
 begin
   r := x.r * y;
   i := x.i * y;
 end;
end;

function PlusReal(x: TComplex; y: TReal): TComplex;
begin
 with result do
 begin
   r := x.r + y;
   i := x.i;
 end;
end;

function ComplexToStr(x: TComplex): string;
begin
 result := FloatToStr(x.r)
   + ' + '
   + FloatToStr(x.i)
   + 'i';
end;

function AbsSquared(x: TComplex): TReal;
begin
 result := x.r * x.r + x.i * x.i;
end;

end.