Question

if Z1 +Z2 = real number then is it mandatary that Z2=cojugate(Z1)

From my thinking it is not because
Z₁=4+2i and Z₂ =3-2i where Z1 is not the conjugate of Z2 but it is clear that Z1+Z2 = 7 a real number

But there is issue in video module of jee complex no

Answer 1

There is no condition that z2 should be the conjugate of z1. It is enough that imaginary parts of z1 and z2 have opposite signs i.e if one is negative the other should be positive.