Theorems · Theorem · field theory
Complex.mk_eq_add_mul_I
∀ (a b : ℝ), { re := a, im := b } = ↑a + ↑b * Complex.I- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- Complex.ofRealstatement · cited by 1,654
- sub_selfproof · cited by 996
- Complex.Istatement and proof · cited by 866
- Complex.mul_reproof · cited by 115
- Complex.mul_improof · cited by 107
- Complex.ext_iffproof · cited by 20
Cited by5
Results whose statement or proof uses this declaration.
- Complex.algHom_extproof · cited by 5
- Complex.restrictScalars_toSpanSingleton'proof · cited by 3
- Complex.integral_boundary_rect_of_hasFDerivAt_real_off_countableproof · cited by 3
- Complex.normSq_add_mul_Iproof · cited by 2
- Complex.arg_eq_neg_pi_div_two_iffproof · cited by 1