Theorems · Theorem · complex analysis
Complex.arg_of_im_nonneg_of_ne_zero
∀ {z : ℂ}, 0 ≤ z.im → z ≠ 0 → z.arg = Real.arccos (z.re / ‖z‖)- Cited by
- 1 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.
Cites11
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
- Complex.restatement · cited by 882
- Complex.imstatement and proof · cited by 591
- Complex.argstatement and proof · cited by 220
- Real.arccosstatement and proof · cited by 90
- Complex.arg_le_piproof · cited by 8
- Complex.cos_argproof · cited by 7
- Complex.arg_nonneg_iffproof · cited by 4
- Real.arccos_cosproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Complex.arg_of_im_posproof · cited by 3