Theorems · Theorem · complex analysis
Complex.exp_eq_exp_re_mul_sin_add_cos
∀ (x : ℂ), Complex.exp x = Complex.exp ↑x.re * (Complex.cos ↑x.im + Complex.sin ↑x.im * Complex.I)
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.ofRealstatement and proof · cited by 1,654
- Complex.restatement and proof · cited by 882
- Complex.Istatement · cited by 866
- Complex.expstatement and proof · cited by 612
- Complex.imstatement and proof · cited by 591
- Complex.cosstatement · cited by 279
- Complex.sinstatement · cited by 258
- Complex.re_add_improof · cited by 41
- Complex.exp_add_mul_Iproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Complex.norm_expproof · cited by 33
- Complex.log_expproof · cited by 4
- Complex.exp_reproof · cited by 2
- Complex.cpow_ofRealproof · cited by 2
- Complex.exp_improof · cited by 1