Theorems · Theorem · complex analysis
Complex.norm_exp
∀ (z : ℂ), ‖Complex.exp z‖ = Real.exp z.re
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- mul_oneproof · cited by 3,885
- Complex.ofRealproof · cited by 1,654
- Complex.restatement and proof · cited by 882
- Real.expstatement and proof · cited by 871
- Complex.Iproof · cited by 866
- Complex.expstatement and proof · cited by 612
- Complex.improof · cited by 591
- Complex.cosproof · cited by 279
- Complex.sinproof · cited by 258
Cited by33
Results whose statement or proof uses this declaration.
- UpperHalfPlane.norm_exp_two_pi_I_lt_oneproof · cited by 7
- Function.Periodic.norm_qParamproof · cited by 6
- norm_cexp_neg_mul_sqproof · cited by 4
- Complex.log_expproof · cited by 4
- Complex.comap_exp_nhds_zeroproof · cited by 4
- integrableOn_exp_mul_complex_Ioiproof · cited by 4
- PhragmenLindelof.quadrant_Iproof · cited by 4
- IsSelfAdjoint.mem_spectrum_eq_reproof · cited by 3
- ProbabilityTheory.hasDerivAt_integral_pow_mul_expproof · cited by 3
- Complex.norm_cpow_of_ne_zeroproof · cited by 2
- norm_jacobiTheta₂_termproof · cited by 2
- GaussianFourier.norm_cexp_neg_mul_sq_add_mul_Iproof · cited by 2