JEE Main 2006Annual, Paper 1MathematicsMediumComplex Numbers and Quadratic Equations264× since 2002If z2+z+1=0{z^2} + z + 1 = 0z2+z+1=0, where z is complex number, then value of (z+1z)2+(z2+1z2)2+(z3+1z3)2+..........+(z6+1z6)2{\left( {z + {1 \over z}} \right)^2} + {\left( {{z^2} + {1 \over {{z^2}}}} \right)^2} + {\left( {{z^3} + {1 \over {{z^3}}}} \right)^2} + .......... + {\left( {{z^6} + {1 \over {{z^6}}}} \right)^2}(z+z1)2+(z2+z21)2+(z3+z31)2+..........+(z6+z61)2 is :AOption A. 18BOption B. 54COption C. 6DOption D. 12CheckSkip · show solution
