Given z is a complex number satisfying z2−z−|z|2+64|z|5=0 and Re(z) ≠12 (where Re(z) denotes real part of z), then |z| is less than
3
4
∵ z2−z=|z2|−64|z|5 = a purely real number
⇒z2−z=¯z2−¯z ⇒(z2−¯z2)−(z−¯z)=0
if z−¯z=0 ⇒z=¯z
⇒ z is purely real number
So put z = x in given equation.
x2−x−|x2|+64x5=0 (if x>0)
(∵ x < 0 not possible)