Z = z iff z is real
SOLUTION: Z = z ------->(EQ 1)
Let Z = a-bι and z=a+bι
By putting the value of z and Z in eq 1,we get.
a-bι = a+bι
a-bι -a-bι =0
∴ z=a+0=a. this is shows that z is real.
Conversly, suppose z is real no.
then z=a+0=a , a ∈ℝ and Z=a-0=a, a ∈ℝ