question_answer2) If\[{{z}^{2}}+z+1=0,\]where z is complex number, then the value of \[{{\left( z+\frac{1}{z} \right)}^{2}}+{{\left( {{z}^{2}}+\frac{1}{{{z}^{2}}} \right)}^{2}}+{{\left( {{z}^{3}}+\frac{1}{{{z}^{3}}} \right)}^{2}}\] \[+......+{{\left( {{z}^{6}}+\frac{1}{{{z}^{6}}} \right)}^{2}}\]is
AIEEE Solved Paper-2006