Theorems · Theorem · complex analysis
Complex.arg_cos_add_sin_mul_I
∀ {θ : ℝ}, θ ∈ Set.Ioc (-Real.pi) Real.pi → (Complex.cos ↑θ + Complex.sin ↑θ * Complex.I).arg = θ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 192 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.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- one_mulproof · cited by 2,841
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- Set.Iocstatement and proof · cited by 971
- Complex.Istatement and proof · cited by 866
- zero_lt_oneproof · cited by 598
- Complex.cosstatement and proof · cited by 279
- Complex.sinstatement and proof · cited by 258
- Complex.argstatement and proof · cited by 220
Cited by3
Results whose statement or proof uses this declaration.
- Circle.arg_expproof · cited by 3
- Complex.range_argproof · cited by 0
- IsPrimitiveRoot.argproof · cited by 0