Theorems · Theorem · complex analysis
Complex.norm_eq_sqrt_sq_add_sq
∀ (z : ℂ), ‖z‖ = √(z.re ^ 2 + z.im ^ 2)
- Defined in
- Mathlib.Analysis.Complex.Norm
- Cited by
- 2 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normstatement · cited by 5,413
- Complex.restatement and proof · cited by 882
- Complex.imstatement and proof · cited by 591
- Real.sqrtstatement and proof · cited by 545
- sqproof · cited by 280
- Complex.norm_defproof · cited by 18
- Complex.normSq_applyproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- ModularGroup.isCompact_truncatedFundamentalDomainproof · cited by 1
- Complex.stolzCone_subset_stolzSet_auxproof · cited by 1