Theorems · Theorem · complex analysis
Complex.angle_exp_exp
∀ (x y : ℝ),
InnerProductGeometry.angle (Complex.exp (↑x * Complex.I)) (Complex.exp (↑y * Complex.I)) =
|toIocMod Real.two_pi_pos (-Real.pi) (x - y)|- Defined in
- Mathlib.Analysis.Complex.Angle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- absstatement and proof · cited by 1,814
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.Istatement and proof · cited by 866
- Complex.expstatement and proof · cited by 612
- Complex.argproof · cited by 220
- InnerProductGeometry.anglestatement · cited by 170
- toIocModstatement and proof · cited by 109
- Real.two_pi_posstatement and proof · cited by 51
- Complex.exp_ne_zeroproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- Complex.angle_exp_oneproof · cited by 1