Assertion: (A) Let $Z_1, Z_2, Z_3$ be the three complex numbers such that  $|3Z_1+1|=|3Z_2+1|=|3Z_3+1|$ and $1+ Z_1+ Z_2+ Z_3=0, then Z_1, Z_2, Z_3$ will represent vertices of an equilateral triangle on the complex plane.
Reason: (R) $Z_1, Z_2 and Z_3$ represent vertices of an equilateral triangle if  ${Z_1}^2+{Z_2}^2+{Z_3}^2+Z_1.Z_2+Z_2.Z_3+Z_3.Z_1=0$