Prove that $ \Delta = (a + \bar{a} - 2)^2$ with (E) : $z^2-2(a-\bar{a})z - |a-1|^2$ in ${\displaystyle \mathbb {C} }$

Question

Prove that $ \Delta = (a + \bar{a} - 2)^2$
with (E) : $z^2-2(a-\bar{a})z - |a-1|^2$; with a $\in {\displaystyle \mathbb {C} }$\{1}

I tried developing $ \Delta $ but I got stuck here : $ \Delta = a² -2\cdot a\bar{a} + (\bar{a})² + 4\cdot|a-1|²$

Thanks to everyone!

Answer 1

Hint: $|a-1|^2 = (a-1)(\bar{a} -1)$.

Expand and continue.

If you're stuck, explain what else you're done.