Correct option (A) z is a purely real number
The equality |z1| + |z2| + |z3| = |z1 + z2 + z3| is true if an only if z1, z2 and z3 are of same signs, that is, either all positive or all negative, that is, they all must be comparable to additive identity. Thus, they all must be real quantities.
Hence, if
then z must also be a real quantity. Therefore, z is a purely real number.
