(* module de manipulation de nombres complexes *)

type complexe = {re :float; im :float} ;;

let unC = {re = 1.; im = 0.};;
let zeroC = {re = 0.; im = 0.};;
let iC = {re = 0.; im = 1.};;
let jC = {re = -0.5; im = 0.866025403784};;

let conjC a = {re = a.re;im = -.a.im};;

let aC a b= {re = a.re+.b.re;im = a.im+.b.im};;

let pC a b= {re = a.re*.b.re-.a.im*.b.im;im = b.re*.a.im+.a.re*.b.im};;

let sC a b= {re = a.re-.b.re;im = a.im-.b.im};;

let dC a b= let module_carre=b.re*.b.re+.b.im*.b.im in
	{re = (a.re*.b.re+.a.im*.b.im)/.module_carre;
	 im = (b.re*.a.im-.a.re*.b.im)/.module_carre}
;;

(* les détails du module sont d'une inutilité profonde, mais c'est l'usage 
de faire cela pour montrer qu'on sait le faire*)
let modarg {re=x; im=y} =
	let modul = let ax=(abs_float x) and ay=(abs_float y) in
		if ax=0. 
		then ay 
		else if ay=0. 
			  then ax
			  else if ax>ay
					 then let q=ay/.ax in ax*.sqrt(1.+.q*.q)
					 else let q=ax/.ay in ay*.sqrt(1.+.q*.q)
	in
	(modul,atan2 x y)
;;


(* un exemple de calcul *)
(* sC conjC(pC jC JC) jc;; *)