Theorems · Theorem · complex analysis
Complex.exp_ofReal_mul_I_re
∀ (x : ℝ), (Complex.exp (↑x * Complex.I)).re = Real.cos x
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 · cited by 5,565
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- Complex.ofRealstatement and proof · cited by 1,654
- sub_selfproof · cited by 996
- Complex.restatement and proof · cited by 882
- Complex.Istatement and proof · cited by 866
- Complex.expstatement · cited by 612
- Real.cosstatement and proof · cited by 424
- Complex.sinproof · cited by 258
Cited by6
Results whose statement or proof uses this declaration.
- Complex.norm_mul_exp_arg_mul_Iproof · cited by 6
- selfAdjoint.norm_sq_expUnitary_sub_oneproof · cited by 3
- Circle.exp_injOn_of_forall_sub_mem_Iooproof · cited by 3
- circleAverage_log_norm_sub_const₁proof · cited by 1
- circleMap_zero_improof · cited by 0
- circleMap_zero_reproof · cited by 0