The centre of a square ABCD is at orign and the point A is represented by z1  The centroid of triangle BCD is represented by

Given A is represented by z1.  Since the diagonals of a square bisect each other at right angles, therefore,∠AOB=  ∠BOC=  ∠COD  =  π2And hence B≡iz1,c≡i2z1  and D≡i3z1∴  Centroid of triangle BCD is represented byiz1−z1−iz13  =  −z13.