if `z-barz=0` then z is purely imaginary

Statement - I : If z = barz then z is purely imaginary Statement- II : If z = -barz then z is purely real

Conjugate of a complex no and its properties. If z, z_1, z_2 are complex no.; then :- (i) bar(barz)=z (ii)z+barz=2Re(z)(iii)z-barz=2i Im(z) (iv)z=barz hArr z is purely real (v) z+barz=0implies z is purely imaginary (vi)zbarz=[Re(z)]^2+[Im(z)]^2

If z^(2) + |z|^(2) = 0 , show that z is purely imaginary.

Prove that : z= -bar(z) iff z is either zero or purely imaginary.

If |z/| barz |- barz |=1+|z|, then prove that z is a purely imaginary number.

If |z/| barz |- barz |=1+|z|, then prove that z is a purely imaginary number.

If |z/| barz |- barz |=1+|z|, then prove that z is a purely imaginary number.

If (z - 1)/(z + 1) is purely imaginary, then |z| is

If a complex number Z is purely imaginary then conjugate of Z is

If a complex number Z is purely imaginary then conjugate of Z is