Theorems · Theorem · complex analysis
Complex.arg_of_im_neg
∀ {z : ℂ}, z.im < 0 → z.arg = -Real.arccos (z.re / ‖z‖)- Cited by
- 3 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.
Cites17
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
- Norm.normstatement · cited by 5,413
- LT.lt.leproof · cited by 2,189
- neg_negproof · cited by 960
- Complex.restatement · cited by 882
- LT.lt.neproof · cited by 872
- Complex.imstatement and proof · cited by 591
- Complex.argstatement and proof · cited by 220
- Real.arccosstatement and proof · cited by 90
- neg_nonnegproof · cited by 60
- Real.cos_negproof · cited by 27
Cited by3
Results whose statement or proof uses this declaration.
- Complex.arg_neg_eq_arg_add_pi_of_im_negproof · cited by 3
- Complex.arg_neg_eq_arg_sub_pi_of_im_posproof · cited by 3
- Complex.arg_eq_nhds_of_im_negproof · cited by 1