Doubt from Complex Number

If the points A(z - i) B(z +1) and C(iz) are the vertices of equilateral triangle then find Re(z) + Im(z)
@Tanmay_1

Z_1^2 +Z_2^2+Z_3^2=Z_1Z_2+Z_2Z_3+Z_3Z_1

compare with final result..

Pls check