norm_num
case mk.mk
c : ℤω
x✝¹ y✝¹ x✝ y✝ : ℤ
⊢ ↑(x✝¹ * x✝ - y✝¹ * y✝) + ↑(x✝¹ * y✝ + y✝¹ * x✝ - y✝¹ * y✝) * complexω =
    (↑x✝¹ + ↑y✝¹ * complexω) * (↑x✝ + ↑y✝ * complexω)
case mk.mk
c : ℤω
x✝¹ y✝¹ x✝ y✝ : ℤ
⊢ ↑x✝¹ * ↑x✝ - ↑y✝¹ * ↑y✝ + (↑x✝¹ * ↑y✝ + ↑y✝¹ * ↑x✝ - ↑y✝¹ * ↑y✝) * complexω =
    (↑x✝¹ + ↑y✝¹ * complexω) * (↑x✝ + ↑y✝ * complexω)