Theorems · Theorem · complex analysis
Complex.arg_mul_cos_add_sin_mul_I_sub
∀ {r : ℝ},
0 < r →
∀ (θ : ℝ),
(↑r * (Complex.cos ↑θ + Complex.sin ↑θ * Complex.I)).arg - θ = 2 * Real.pi * ↑⌊(Real.pi - θ) / (2 * Real.pi)⌋- Cited by
- 1 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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 · cited by 5,565
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement · cited by 1,654
- pow_oneproof · cited by 894
- Complex.Istatement · cited by 866
- Complex.cosstatement · cited by 279
- Complex.sinstatement · cited by 258
- Int.floorstatement and proof · cited by 225
- Complex.argstatement · cited by 220
Cited by1
Results whose statement or proof uses this declaration.
- Complex.arg_cos_add_sin_mul_I_subproof · cited by 0