Theorems · Theorem · field theory
Complex.conj_eq_iff_im
∀ {z : ℂ}, (starRingEnd ℂ) z = z ↔ z.im = 0- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- RingHomstatement · cited by 10,189
- Complexstatement and proof · cited by 5,565
- starRingEndstatement and proof · cited by 671
- Complex.imstatement and proof · cited by 591
- Complex.extproof · cited by 28
- neg_eq_iff_add_eq_zeroproof · cited by 16
- add_self_eq_zeroproof · cited by 7
Cited by9
Results whose statement or proof uses this declaration.
- NumberField.is_primitive_element_of_infinitePlace_ltproof · cited by 3
- Complex.eq_re_of_ofReal_leproof · cited by 2
- NumberField.InfinitePlace.IsPrimitiveRoot.nrRealPlaces_eq_zero_of_two_ltproof · cited by 2
- Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_invproof · cited by 2
- NumberField.sign_discrproof · cited by 1
- NumberField.ComplexEmbedding.IsReal.coe_embedding_applyproof · cited by 1
- Polynomial.mul_star_dvd_of_aeval_eq_zero_im_ne_zeroproof · cited by 1
- UpperHalfPlane.dist_triangleproof · cited by 0
- NumberField.mixedEmbedding.disjoint_span_commMap_kerproof · cited by 0