Theorems · Theorem · complex analysis
Complex.arg_eq_pi_iff
∀ {z : ℂ}, z.arg = Real.pi ↔ z.re < 0 ∧ z.im = 0- Cited by
- 7 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- Norm.normproof · cited by 5,413
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealproof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- neg_negproof · cited by 960
- Complex.restatement and proof · cited by 882
- Complex.Iproof · cited by 866
- Complex.imstatement and proof · cited by 591
Cited by7
Results whose statement or proof uses this declaration.
- Complex.arg_ofReal_of_negproof · cited by 5
- fourier_gaussian_pi'proof · cited by 2
- Polynomial.cyclotomic_eval_lt_add_one_pow_totientproof · cited by 1
- Complex.arg_eq_pi_iff_lt_zeroproof · cited by 0
- Complex.tendsto_log_nhdsWithin_im_nonneg_of_re_neg_of_im_zeroproof · cited by 0
- Complex.arg_lt_pi_iffproof · cited by 0
- Complex.tendsto_arg_nhdsWithin_im_nonneg_of_re_neg_of_im_zeroproof · cited by 0