Theorems · Theorem · complex analysis
Complex.arg_mul_coe_angle
∀ {x y : ℂ}, x ≠ 0 → y ≠ 0 → ↑(x * y).arg = ↑x.arg + ↑y.arg- Cited by
- 6 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- Complex.ofRealproof · cited by 1,654
- Complex.Iproof · cited by 866
- Complex.expproof · cited by 612
- Real.Anglestatement and proof · cited by 518
- Real.sinproof · cited by 389
- mul_posproof · cited by 374
- add_mulproof · cited by 363
Cited by6
Results whose statement or proof uses this declaration.
- Orientation.oangle_addproof · cited by 5
- Orientation.oangle_rotation_leftproof · cited by 3
- Orientation.oangle_rotation_rightproof · cited by 3
- Complex.arg_mul_eq_add_arg_iffproof · cited by 2
- Complex.arg_pow_coe_angleproof · cited by 2
- Complex.arg_div_coe_angleproof · cited by 1