unit Cmplx;

interface
uses math;
type complex = record
        re,im: extended;
end;

function abs (a:complex):extended;
function arg (a:complex):extended;
function conj (a:complex):complex;
function add (a,b:complex):complex;
function sub (a,b:complex):complex;
function mult (a,b:complex):complex;
function divi (a,b:complex):complex;
function csqrt (a:complex):complex;
function pow (a:complex; b: extended):complex; overload;
function pow ( a:complex; b: complex) : complex; overload;
function csin (a:complex):complex;
function ccos (a:complex):complex;
function ctan (a:complex):complex;

implementation

function abs (a:complex):extended;
begin
        abs:=sqrt(Sqr(a.re)+Sqr(a.im));
end;

function arg (a:complex):extended;
begin
        if a.re<>0 then arg:=arctan(a.im/a.re) else
                if a.im>0 then arg:=pi/2 else arg:=-pi/2;
end;

function conj (a:complex):complex;
begin
        conj.re:=a.re;
        conj.im:=-a.im;
end;

function add (a,b:complex):complex;
begin
        add.re:=a.re + b.re;
        add.im:=a.im + b.im;
end;

function sub (a,b:complex):complex;
begin
        sub.re:=a.re - b.re;
        sub.im:=a.im - b.im;
end;

function mult (a,b:complex):complex;
begin
        mult.re:=a.re*b.re - a.im*b.im;
        mult.im:=a.im*b.re + b.im*a.re;
end;

function divi (a,b:complex):complex;
var k:extended;
begin
        k:=b.re*b.re+b.im*b.im;
        if (k=0) then {write cannot divide by zero} else begin
                divi.re:=(a.re*b.re + a.im*b.im)/k;
                divi.im:=(a.im*b.re - a.re*b.im)/k;
        end;
end;

function csqrt (a:complex):complex;
var j,k:extended;
begin
        k:=arg(a)/2;
        j:=sqrt(abs(a));
        csqrt.re:=j*cos(k);
        csqrt.im:=j*sin(k);
end;

function pow (a:complex; b: extended):complex; overload;
var j,k:extended;
begin
        k:=arg(a)*b;
        j:=Power(abs(a),b);
        pow.re:=j*cos(k);
        pow.im:=j*sin(k);
end;

function  pow ( a:complex; b: complex) : complex; overload;
Begin

End;

function csin (a:complex):complex;
begin
        csin.re:=sin(a.re)*cosh(a.im);
        csin.im:=cos(a.re)*sinh(a.im);
end;

function ccos (a:complex):complex;
begin
        ccos.re:=cos(a.re)*cosh(a.im);
        ccos.im:=-sin(a.re)*sinh(a.im);
end;

function ctan (a:complex):complex;
begin
        ctan:=divi(csin(a),ccos(a));
end;

end.