If \( z \) is a complex number satisfying \( z+z^{-1}=1 \) then \( z^{n}+z^{-n}, n \in N \), has...
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0If \( z \) is a complex number satisfying \( z+z^{-1}=1 \) then \( z^{n}+z^{-n}, n \in N \), has the value
(a) \( 2(-1)^{n} \) when \( n \) is a multiple of 3
(b) \( (-1)^{n-1} \) when \( n \) is not a multiple of 3
(c) \( (-1)^{n+1} \) when \( n \) is a multiple of 3
(d) 0 when \( n \) is not a multiple of 3
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