simp only [complexα]
case a
a b c : ℤα
⊢ complexα.re * complexα.im + complexα.im * complexα.re = (complexα - 2).im
case a
a b c : ℤα
⊢ 1 / 2 * (rt7 / 2) + rt7 / 2 * (1 / 2) = ({ re := 1 / 2, im := rt7 / 2 } - 2).im