Theorems · Theorem · complex analysis
Complex.arg_mul_cos_add_sin_mul_I
∀ {r : ℝ},
0 < r → ∀ {θ : ℝ}, θ ∈ Set.Ioc (-Real.pi) Real.pi → (↑r * (Complex.cos ↑θ + Complex.sin ↑θ * Complex.I)).arg = θ- Cited by
- 5 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites48
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 · cited by 5,565
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- Set.Iccproof · cited by 1,702
- Complex.ofRealstatement and proof · cited by 1,654
- LT.lt.ne'proof · cited by 1,417
- Set.Iocstatement and proof · cited by 971
Cited by5
Results whose statement or proof uses this declaration.
- Complex.arg_real_mulproof · cited by 11
- Complex.arg_mem_Iocproof · cited by 6
- Complex.log_expproof · cited by 4
- Complex.arg_cos_add_sin_mul_Iproof · cited by 3
- Complex.arg_expproof · cited by 3