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Question

If z2z+1=0 then znzn, where n is a multiple of 3, is

A
2(1)n
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B
0
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C
(1)n+1
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D
none of these
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Solution

The correct option is B 0
z2z+1=0
Here, we can say that
z is cube root of unity
z=ω,ω2
Considering z=ω
znzn=ωnωn
Now ωn=1 when n=3k
ωn=1,ωn=1ωn=11=1
ωnωn=0
znzn=0

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