Theorems · Theorem · complex analysis
Complex.norm_mul_cos_arg
∀ (x : ℂ), ‖x‖ * Real.cos x.arg = x.re
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · 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
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- Complex.ofRealproof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- sub_selfproof · cited by 996
- sub_zeroproof · cited by 938
- Complex.restatement and proof · cited by 882
Cited by4
Results whose statement or proof uses this declaration.
- Complex.cpow_inv_two_reproof · cited by 6
- Complex.cpow_inv_two_im_eq_sqrtproof · cited by 4
- Complex.cpow_inv_two_im_eq_neg_sqrtproof · cited by 2
- Complex.abs_cpow_inv_two_improof · cited by 0