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Complex Numbers question

2006 · Shift 0 · Q67

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PYQ Library
JEE Main
Mathematics
Complex Numbers
2006 · Shift 0 · Q67

Complex Numbers question

2006 · Shift 0 · Q67

JEE MainMathematicsComplex NumbersMCQ+4 / −1

If

{z^2} + z + 1 = 0

, where z is complex number, then value of

{\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}

is :

A
18
B
54
C
6
D
12

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