Theorems · Theorem · real analysis
Complex.norm_cpow_of_ne_zero
∀ {z : ℂ}, z ≠ 0 → ∀ (w : ℂ), ‖z ^ w‖ = ‖z‖ ^ w.re / Real.exp (z.arg * w.im)- Cited by
- 2 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.
Cites17
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
- Real.logproof · cited by 939
- Complex.restatement and proof · cited by 882
- Real.expstatement and proof · cited by 871
- Complex.imstatement and proof · cited by 591
- Complex.argstatement and proof · cited by 220
- Complex.logproof · cited by 187
- norm_pos_iffproof · cited by 168
- Complex.mul_reproof · cited by 115
- Real.rpow_def_of_posproof · cited by 35
Cited by2
Results whose statement or proof uses this declaration.
- Complex.norm_cpow_eq_rpow_re_of_posproof · cited by 21
- Complex.norm_cpow_of_impproof · cited by 4