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

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