Theorems · Theorem · field theory
Complex.mul_im
∀ (z w : ℂ), (z * w).im = z.re * w.im + z.im * w.re
- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 107 results in Mathlib
- Foundations
- Depth 93 from the axioms, rests on 1,611 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Complex.restatement · cited by 882
- Complex.imstatement · cited by 591
Cited by107
Results whose statement or proof uses this declaration.
- Complex.ofReal_mulproof · cited by 180
- Complex.re_add_improof · cited by 41
- Complex.I_mul_Iproof · cited by 35
- Complex.inv_improof · cited by 13
- Complex.im_ofReal_mulproof · cited by 10
- Complex.log_improof · cited by 9
- UpperHalfPlane.norm_exp_two_pi_I_lt_oneproof · cited by 7
- Complex.norm_mul_exp_arg_mul_Iproof · cited by 6
- Function.Periodic.norm_qParamproof · cited by 6
- Complex.norm_cos_add_sin_mul_Iproof · cited by 6
- Complex.sin_mul_Iproof · cited by 5
- Complex.mk_eq_add_mul_Iproof · cited by 5