proposition: Lemma ImJ_sub (x : R[i]) : (Im x)%:C = (x^*%C - x) / 2%:R * 'i%C.
proof: Proof. case: x => a b; simpc; rewrite [0 ^+ 2]mul0r addr0 /=. rewrite -!mulr2n -mulr_natr -mulrA [_ * (_ / _)]mulrA. by rewrite divff ?mulr1 ?opprK // -natrM pnatr_eq0. Qed.
imports: HB(structures) mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(bigop order ssralg ssrint div ssrnum rat poly closed_field) mathcomp(polyrcf matrix mxalgebra tuple mxpoly zmodp binomial realalg) mathcomp(mxpoly)