Theorems · Theorem · complex analysis
RCLike.norm_to_complex
∀ {𝕜 : Type u_2} [inst : RCLike 𝕜] (a : 𝕜), ‖↑(RCLike.re a) + ↑(RCLike.im a) * Complex.I‖ = ‖a‖- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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 and proof · cited by 25,697
- Complexstatement · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapproof · cited by 4,706
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- add_zeroproof · cited by 2,707
- absproof · cited by 1,814
- Complex.ofRealstatement and proof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
Cited by1
Results whose statement or proof uses this declaration.
- RCLike.sqrt_eq_real_add_iteproof · cited by 0