Theorems · Theorem · field theory
Complex.normSq_apply
∀ (z : ℂ), Complex.normSq z = z.re * z.re + z.im * z.im
- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 8 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Complex.restatement · cited by 882
- MonoidWithZeroHomstatement · cited by 704
- Complex.imstatement · cited by 591
- Complex.normSqstatement · cited by 103
Cited by8
Results whose statement or proof uses this declaration.
- Complex.abs_im_le_normproof · cited by 6
- Complex.abs_re_lt_normproof · cited by 2
- Complex.norm_eq_sqrt_sq_add_sqproof · cited by 2
- Complex.norm_sub_one_sq_eq_of_norm_eq_oneproof · cited by 2
- UpperHalfPlane.gl_smul_eq_self_iff_dist_sq_eqproof · cited by 1
- Algebra.norm_complex_applyproof · cited by 1
- Complex.sq_norm_sub_sq_reproof · cited by 1
- LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_reproof · cited by 1