Theorems · Theorem · complex analysis
Complex.log_re
∀ (x : ℂ), (Complex.log x).re = Real.log ‖x‖
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- Complex.ofRealproof · cited by 1,654
- sub_selfproof · cited by 996
- Real.logstatement and proof · cited by 939
- Complex.restatement · cited by 882
- Complex.Iproof · cited by 866
- Complex.argproof · cited by 220
Cited by7
Results whose statement or proof uses this declaration.
- Complex.ofReal_logproof · cited by 14
- Complex.log_ofReal_reproof · cited by 2
- Function.Periodic.im_invQParamproof · cited by 2
- Complex.norm_cpow_of_ne_zeroproof · cited by 2
- expUnitary_argSelfAdjointproof · cited by 2
- Complex.log_mul_eq_add_log_iffproof · cited by 2
- Complex.cpow_ofRealproof · cited by 2