have hA : A.re = 0 := by
  simp only [← hu, hv1, hx, add_zero, MulZeroClass.zero_mul, Zsqrtd.mul_re, MulZeroClass.mul_zero,
    Zsqrtd.intCast_im]
case intro.intro.intro
x A : ℤ√(-3)
hx : x.re = 0
u : (ℤ√(-3))ˣ
hu : x * ↑u = A
v : ℤ
hv1 : ↑u = ↑v
hv2 : |v| = 1
⊢ x = A ∨ x = star A
case intro.intro.intro
x A : ℤ√(-3)
hx : x.re = 0
u : (ℤ√(-3))ˣ
hu : x * ↑u = A
v : ℤ
hv1 : ↑u = ↑v
hv2 : |v| = 1
hA : A.re = 0
⊢ x = A ∨ x = star A