Theorems · Theorem · complex analysis
RCLike.sqrt_eq_real_add_ite
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {a : 𝕜},
RCLike.sqrt a =
↑√((‖a‖ + RCLike.re a) / 2) + (if 0 ≤ RCLike.im a then 1 else -1) * ↑√((‖a‖ - RCLike.re a) / 2) * RCLike.I- Defined in
- Mathlib.Analysis.RCLike.Sqrt
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
Around this declaration
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Cites50
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
- Complexproof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- AddMonoidHomstatement · cited by 3,230
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
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