2015/061) Simplify $((-1)+\frac{i\sqrt{2}}{3})^2 + ((-1)-\frac{i\sqrt{2}}{3})^2$

we know

$(a+b)^2 + (a-b)^2 = 2 (a^2+b^2)$

gives $((-1)+\frac{i\sqrt{2}}{3})^2 + ((-1)-\frac{i\sqrt{2}}{3})^2$

  =$2((-1)^2+(\frac{i\sqrt{2}}{3})^2)$

 $= 2 ( 1- \frac{2}{9}) = \frac{14}{9}$