apply JoinedIn.ofLine cont.continuousOn (by simp [f]) (by simp [f])
case neg
w : ℂ
hw : ¬w = 1 ∧ 0 < w.re
w_im : ¬w.im = 0
f : ℝ → ℂ := fun t => w * ↑t + 2 * (1 - ↑t)
cont : Continuous f
⊢ JoinedIn {z | z ≠ 1 ∧ 0 < z.re} 2 w
case neg
w : ℂ
hw : ¬w = 1 ∧ 0 < w.re
w_im : ¬w.im = 0
f : ℝ → ℂ := fun t => w * ↑t + 2 * (1 - ↑t)
cont : Continuous f
⊢ f '' unitInterval ⊆ {z | z ≠ 1 ∧ 0 < z.re}