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Theorems · Theorem · complex analysis

Complex.norm_I

‖Complex.I‖ = 1
Defined in
Mathlib.Analysis.Complex.Norm
Cited by
46 results in Mathlib
Foundations
Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
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CircleIntegrable.out · cited by 5CircleIntegrable.outNumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis · cited by 4mixedEmbedding.volume_fun…Complex.abs_im_lt_norm · cited by 3Complex.abs_im_lt_normComplex.arg_neg_I · cited by 2Complex.arg_neg_Inorm_jacobiTheta₂_term_fderiv_le · cited by 2norm_jacobiTheta₂_term_fd…summable_jacobiTheta₂'_term_iff · cited by 2summable_jacobiTheta₂'_te…hasSum_two_pi_I_cauchyPowerSeries_integral · cited by 2hasSum_two_pi_I_cauchyPow…HurwitzZeta.hasSum_int_completedSinZeta · cited by 2HurwitzZeta.hasSum_int_co…circleIntegrable_iff · cited by 2circleIntegrable_iffComplex.arg_I · cited by 2Complex.arg_IsummableLocallyUniformlyOn_iteratedDerivWithin_smul_cexp · cited by 2summableLocallyUniformlyO…Complex.imCLM_norm · cited by 2Complex.imCLM_normTorusIntegrable.function_integrable · cited by 2TorusIntegrable.function_…VectorFourier.norm_fourierPowSMulRight_le · cited by 2VectorFourier.norm_fourie…VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight · cited by 2VectorFourier.norm_iterat…Real · cited by 25697RealComplex · cited by 5565ComplexNorm.norm · cited by 5413Norm.normComplex.I · cited by 866Complex.IReal.sqrt · cited by 545Real.sqrtReal.sqrt_one · cited by 16Real.sqrt_oneComplex.normSq_I · cited by 2Complex.normSq_IComplex.norm_ICITED BYCITES

Cites7

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Cited by46

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