Theorems · Theorem · complex analysis
Complex.cos_arg
∀ {x : ℂ}, x ≠ 0 → Real.cos x.arg = x.re / ‖x‖- Cited by
- 7 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
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 and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- LT.lt.leproof · cited by 2,189
- neg_negproof · cited by 960
- one_ne_zeroproof · cited by 885
- Complex.restatement and proof · cited by 882
- ne_of_gtproof · cited by 637
- div_oneproof · cited by 629
- Complex.improof · cited by 591
Cited by7
Results whose statement or proof uses this declaration.
- Complex.exp_logproof · cited by 14
- Complex.norm_mul_exp_arg_mul_Iproof · cited by 6
- Complex.angle_eq_abs_argproof · cited by 4
- Complex.arg_of_im_negproof · cited by 3
- Complex.arg_of_im_nonneg_of_ne_zeroproof · cited by 1
- Orientation.inner_eq_norm_mul_norm_mul_cos_oangleproof · cited by 1
- Complex.tan_argproof · cited by 0