Number of complex numbers satisfying equation `z^3 = bar z & arg(z+1) = pi/4` simultaneously is

Number of complex numbers satisfying z^(3)=bar(z) is

Number of imaginary complex numbers satisfying the equation, z^2=bar(z)2^(1-|z|) is

Number of imaginary complex numbers satisfying the equation, z^2=bar(z)2^(1-|z|) is

The number of unimodular complex numbers z satisfying the equation z^(2)+bar(z)=0 is

The complex number z satisfying the equation |z-i|=|z+1|=1

The complex number z satisfying the equation |z-i|=|z+1|=1 is

The complex number z satisfying |z+1|=|z-1| and arg (z-1)/(z+1)=pi/4 , is

Number of complex number satisfying |z+2|+|z-2|=8 and |z-1|+|z+1|=2 simultaneously is:

Number of imaginary complex numbers satisfying the equation, z^2=bar(z)2^(1-|z|) is (A) 0 (B) 1 (C) 2 (D) 3