Theorems · Theorem · complex analysis
Complex.normSq_eq_norm_sq
∀ (z : ℂ), Complex.normSq z = ‖z‖ ^ 2
- Defined in
- Mathlib.Analysis.Complex.Norm
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Complexstatement and proof · cited by 5,565
- Norm.normstatement · cited by 5,413
- MonoidWithZeroHomstatement · cited by 704
- Real.sqrtproof · cited by 545
- sqproof · cited by 280
- Complex.normSqstatement and proof · cited by 103
- Real.mul_self_sqrtproof · cited by 23
- Complex.norm_defproof · cited by 18
- Complex.normSq_nonnegproof · cited by 14
Cited by14
Results whose statement or proof uses this declaration.
- Complex.sq_normproof · cited by 7
- Complex.angle_eq_abs_argproof · cited by 4
- Complex.meromorphicOrderAt_canonicalFactorproof · cited by 3
- ModularGroup.cases_of_mem_fd_smul_mem_fdproof · cited by 2
- Complex.one_le_normSq_iffproof · cited by 2
- Complex.one_lt_normSq_iffproof · cited by 2
- Complex.log_inv_eq_iteproof · cited by 2
- Circle.normSq_coeproof · cited by 2
- UpperHalfPlane.gl_smul_eq_self_iff_dist_sq_eqproof · cited by 1
- ModularGroup.exists_one_half_le_im_smul_and_norm_denom_leproof · cited by 1
- LinearIsometry.im_apply_eq_improof · cited by 1
- ModularGroup.coe_truncatedFundamentalDomainproof · cited by 1