question_answer

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

A)  18                   

B)  12           

C)  54                   

D)  6