Theorems · Theorem · field theory
Complex.im_ofReal_mul
∀ (r : ℝ) (z : ℂ), (↑r * z).im = r * z.im
- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 10 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.
Cites8
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 and proof · cited by 5,565
- add_zeroproof · cited by 2,707
- Complex.ofRealstatement · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- Complex.reproof · cited by 882
- Complex.imstatement and proof · cited by 591
- Complex.mul_improof · cited by 107
Cited by10
Results whose statement or proof uses this declaration.
- Complex.Gamma_ne_zeroproof · cited by 6
- Complex.arg_mul_cos_add_sin_mul_Iproof · cited by 5
- PhragmenLindelof.horizontal_stripproof · cited by 3
- norm_jacobiTheta₂_termproof · cited by 2
- Complex.cpow_ofRealproof · cited by 2
- Complex.ofReal_mul'proof · cited by 2
- ModularGroup.tendsto_normSq_coprime_pairproof · cited by 1
- EisensteinSeries.auxbound1proof · cited by 1
- EisensteinSeries.auxbound2proof · cited by 1
- Function.Periodic.norm_qParam_le_of_one_half_le_improof · cited by 0