Theorems · Theorem · complex analysis
Complex.arg_mul_cos_add_sin_mul_I_eq_toIocMod
∀ {r : ℝ},
0 < r → ∀ (θ : ℝ), (↑r * (Complex.cos ↑θ + Complex.sin ↑θ * Complex.I)).arg = toIocMod Real.two_pi_pos (-Real.pi) θ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.Istatement and proof · cited by 866
- Complex.cosstatement and proof · cited by 279
- Complex.sinstatement and proof · cited by 258
- Complex.argstatement and proof · cited by 220
- toIocModstatement and proof · cited by 109
- Real.two_pi_posstatement and proof · cited by 51
- Complex.exp_mul_Iproof · cited by 17
- Complex.arg_real_mulproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Complex.arg_mul_cos_add_sin_mul_I_coe_angleproof · cited by 2
- Complex.arg_mul_cos_add_sin_mul_I_subproof · cited by 1
- Complex.arg_cos_add_sin_mul_I_eq_toIocModproof · cited by 0