Theorems · Theorem · real analysis
Complex.norm_cpow_of_imp
∀ {z w : ℂ}, (z = 0 → w.re = 0 → w = 0) → ‖z ^ w‖ = ‖z‖ ^ w.re / Real.exp (z.arg * w.im)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- eq_or_neproof · cited by 1,117
- Complex.restatement and proof · cited by 882
- Real.expstatement and proof · cited by 871
- Complex.imstatement and proof · cited by 591
- norm_zeroproof · cited by 366
- div_selfproof · cited by 237
- zero_divproof · cited by 222
- Complex.argstatement and proof · cited by 220
Cited by4
Results whose statement or proof uses this declaration.
- Complex.norm_cpow_eq_rpow_re_of_nonnegproof · cited by 4
- Complex.norm_cpow_leproof · cited by 2
- Complex.norm_cpow_realproof · cited by 2
- Complex.isTheta_cpow_rpowproof · cited by 1