Let S be the set of all complex numbers z satisfying z2+z+1=1 . Then which of the following  statements is/are TRUE ?

z2+z+1=1⇒ z+122+34=1⇒1=z+122+34≤z+122+34⇒ 1≤z+122+34 ⇒z+122≥14⇒z+12≥12 also z2+z+1=1≥∥z2+z|−1|     sincez1-z2≤ z1+z2 ⇒z2+z−1≤1⇒z2+z≤2⇒∥z2|−|z||≤z2+z≤2⇒r2−r≤2     where r=z ⇒r2-r≤2⇒r2-r-2≤0⇒r-2r+1≤0⇒r-2≤0⇒ r=|z|≤2;∀z∈S Also we can always find root of the equation z2+z+1=eiθ;∀θ∈R Hence set 'S' is infinite