Theorems · Theorem · complex analysis
Complex.arg_mul_cos_add_sin_mul_I_coe_angle
∀ {r : ℝ}, 0 < r → ∀ (θ : Real.Angle), ↑(↑r * (↑θ.cos + ↑θ.sin * Complex.I)).arg = θ- Cited by
- 2 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.
Cites15
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
- Real.piproof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.Istatement and proof · cited by 866
- Real.Anglestatement and proof · cited by 518
- Real.Angle.coestatement and proof · cited by 360
- Complex.argstatement and proof · cited by 220
- Real.Angle.cosstatement · cited by 77
- Real.Angle.sinstatement · cited by 75
- Complex.ofReal_cosproof · cited by 43
- Complex.ofReal_sinproof · cited by 40
Cited by2
Results whose statement or proof uses this declaration.
- Complex.arg_mul_coe_angleproof · cited by 6
- Complex.arg_cos_add_sin_mul_I_coe_angleproof · cited by 1