Theorems · Theorem · complex analysis
Complex.exp_mul_I
∀ (x : ℂ), Complex.exp (x * Complex.I) = Complex.cos x + Complex.sin x * Complex.I
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- Complex.Istatement · cited by 866
- Complex.expstatement · cited by 612
- Complex.cosstatement · cited by 279
- Complex.sinstatement · cited by 258
- Complex.cos_add_sin_Iproof · cited by 4
Cited by17
Results whose statement or proof uses this declaration.
- Complex.norm_exp_ofReal_mul_Iproof · cited by 14
- Complex.norm_mul_cos_add_sin_mul_Iproof · cited by 8
- Complex.exp_ofReal_mul_I_reproof · cited by 6
- Complex.exp_antiperiodicproof · cited by 5
- Complex.exp_add_mul_Iproof · cited by 4
- Complex.exp_ofReal_mul_I_improof · cited by 4
- Complex.arg_mul_cos_add_sin_mul_I_eq_toIocModproof · cited by 3
- Circle.arg_expproof · cited by 3
- Real.Angle.coe_toCircleproof · cited by 3
- Complex.arg_expproof · cited by 3
- Real.Angle.arg_toCircleproof · cited by 2
- Complex.norm_sub_mem_Icc_angleproof · cited by 2