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

(** ** Question -1: The real part of product *)
Lemma algReM (x y : algC) :
'Re (x * y) = 'Re x * 'Re y - 'Im x * 'Im y.