Theorems · Theorem · field theory
Complex.div_ofReal_im
∀ (z : ℂ) (x : ℝ), (z / ↑x).im = z.im / x
- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Complex.ofRealstatement · cited by 1,654
- Complex.reproof · cited by 882
- Complex.imstatement and proof · cited by 591
- Complex.div_ofRealproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- UpperHalfPlane.tendsto_smul_atImInftyproof · cited by 2
- Function.Periodic.im_invQParamproof · cited by 2
- summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexpproof · cited by 2
- UpperHalfPlane.gl_smul_eq_self_iff_dist_sq_eqproof · cited by 1
- RCLike.sqrt_eq_real_add_iteproof · cited by 0
- UpperHalfPlane.forall_smul_eq_self_iff_mem_centerproof · cited by 0
- UpperHalfPlane.exists_gl_smul_eq_self_iff_trace_eq_zeroproof · cited by 0