z is purely real
z is purely imaginary
Either z is purely real or purely imaginary
Let z = x + iy, then its conjugate \bar{z} = x - iy Given that z2=(¯z)2 ⇒ x2−y2+2ixy=x2−y2−2ixy ⇒ 4ixy=0 If x ≠ then y = 0and if y ≠ 0 then x = 0
If z is a complex number such that z2−z+1=0 , then z2011