The number of complex numbers z which satisfy z2+2|z|2=2 is

As z2=21−|z|2 is real z is either purely real or purely imaginary.If z is purely real, thenz2=21−z2⇒z=±23TIP If z is purely imaginary, then |z|2=−z2.in this case z2=21+z2⇒z=±2iThus, there are four complex numbers satisfying          z2+2|z|2=2