If z^2 + z + 1 = 0, where z is a complex number

If z2 + z + 1 = 0, where z is a complex number, then the value of

(z + 1/z)2 + (z2 + 1/z2)2 + ... + (z6 + 1/z6)2

  1. 6
  2. 12
  3. 18
  4. 54

Answer

z2 + z + 1 = 0

This implies, z = w, w2

(z + 1/z)2 + (z2 + 1/z2)2 + ... + (z6 + 1/z6)2 

= 4(w + w2)2 + 2(w3 + w3)2

= 4(-1)2 + 2(22)

= 12

The correct option is B.