no goals
E : Type ?u.690001
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℂ E
f : ℂ →+* ℂ
hf : Continuous ↑f
⊢ f = RingHom.id ℂ ∨ f = starRingEnd ℂ
simpa only [FunLike.ext_iff] using real_algHom_eq_id_or_conj (AlgHom.mk' f (map_real_smul f hf))