Theorems · Theorem · complex analysis
Complex.tan_eq_zero_iff
∀ {θ : ℂ}, Complex.tan θ = 0 ↔ ∃ k, ↑k * ↑Real.pi / 2 = θThe tangent of a complex number is equal to zero
iff this number is equal to k * π / 2 for an integer k.
Note that this lemma takes into account that we use zero as the junk value for division by zero.
See also Complex.tan_eq_zero_iff'.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- mul_assocproof · cited by 1,667
- Complex.ofRealstatement and proof · cited by 1,654
- one_ne_zeroproof · cited by 885
- div_oneproof · cited by 629
- Complex.cosproof · cited by 279
Cited by4
Results whose statement or proof uses this declaration.
- Complex.tan_eq_zero_of_cos_eq_zeroproof · cited by 2
- Real.tan_eq_zero_iffproof · cited by 1
- Complex.tan_ne_zero_iffproof · cited by 1
- Complex.tan_int_mul_pi_div_twoproof · cited by 1