Theorems · Theorem · complex analysis
Complex.cos_add_sin_I
∀ (x : ℂ), Complex.cos x + Complex.sin x * Complex.I = Complex.exp (x * Complex.I)
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 866
- Complex.expstatement · cited by 612
- Complex.cosstatement and proof · cited by 279
- Complex.sinstatement and proof · cited by 258
- Complex.coshproof · cited by 118
- Complex.cosh_mul_Iproof · cited by 11
- Complex.sinh_mul_Iproof · cited by 10
- Complex.cosh_add_sinhproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Complex.exp_mul_Iproof · cited by 17
- Complex.arg_mul_coe_angleproof · cited by 6
- Complex.exp_pi_div_two_mul_Iproof · cited by 1
- Complex.exp_neg_pi_div_two_mul_Iproof · cited by 1