Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Open Scope ring_scope.
(** Starting from cyril exercise *)
Section PreliminaryLemmas.

Lemma algRe_div (x y : algC) :
'Re (x/y) = ('Re x * 'Re y + 'Im x * 'Im y) / `|y| ^+ 2.