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Question

If z2+z+1=0, where z is a complex number, then the value of (z+1z)2+(z2+1z2)2+(z3+1z3)2+....+(z6+1z6)2 is

A
18
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B
54
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C
6
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D
12
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Solution

The correct option is D 12
z2+z+1=0z=ω,ω2
(z+1z)2+(z2+1z2)2+......(z6+1z6)2
=(ω+ω2)2+(ω+ω2)2+(ω3+1ω3)2+(ω+ω2)2+(ω+ω2)2+(ω6+1ω6)2
4(ω+ω2)2+2(ω3+1ω3)2=4(1)+2(22)=4+8=12.

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