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

(** ** Question 0: The imaginary part of product *)
Lemma algImM (x y : algC) : 'Im (x * y) = 'Re x * 'Im y + 'Re y * 'Im x.