Theorems · Theorem · complex analysis
Complex.norm_mul_exp_arg_mul_I
∀ (x : ℂ), ↑‖x‖ * Complex.exp (↑x.arg * Complex.I) = x
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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.normstatement and proof · cited by 5,413
- add_zeroproof · cited by 2,707
- mul_commproof · cited by 2,262
- Complex.ofRealstatement and proof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- eq_or_neproof · cited by 1,117
- sub_zeroproof · cited by 938
- Complex.reproof · cited by 882
- Complex.Istatement and proof · cited by 866
- Complex.expstatement and proof · cited by 612
Cited by6
Results whose statement or proof uses this declaration.
- Complex.norm_mul_cos_add_sin_mul_Iproof · cited by 8
- Complex.arg_mul_coe_angleproof · cited by 6
- Complex.ext_norm_argproof · cited by 3
- Complex.norm_eq_one_iffproof · cited by 1
- le_re_herglotzRieszKernelproof · cited by 0
- re_herglotzRieszKernel_leproof · cited by 0