a) Let be two nonzero complex numbers $ a,b. $ Show that the area of the triangle formed by the representations of the affixes $ 0,a,b $ in the complex plane is $ \frac{1}{4}\left| \overline{a} b-a\overline{b} \right| . $ b) Let be an equilateral triangle $ ABC, $ its circumcircle $ \mathcal{C} , $ its circumcenter $ O, $ and two distinct points $ P_1,P_2 $ in the interior of $ \mathcal{C} . $ Prove that we can form two triangles with sides $ P_1A,P_1B,P_1C, $ respectively, $ P_2A,P_2B,P_2C, $ whose areas are equal if and only if $ OP_1=OP_2. $