Solve the equation `z^2 = bar(z)`

Solve that equation z^2+|z|=0 , where z is a complex number.

The number of solutions of the equation z^2+ bar z=0 is :

Solve the equation |z|=z+1+2idot

In complex plane, the equation |z+ bar z|=|z- bar z| represents :

Solve the equation |z|+z=2+i, where z = x + iy.

Let a ,b and c be any three nonzero complex number. If |z|=1 and' z ' satisfies the equation a z^2+b z+c=0, prove that a .bar a = c .bar c and |a||b|= sqrt(a c( bar b )^2)