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If z^2-z+1=0 then z^n-z^-n , where n is a multiple of 3, is a 2(-1)^n. b 0. c (-1)^n+1 d none of these A Das Gupta Complex Number Que 34

If z^2-z+1=0 then z^n-z^-n , where n is a multiple of 3, is 
a 2(-1)^n.   b 0.   c (-1)^n+1 d none of these
 
A Das Gupta Complex Number Que 34

Grade:11

1 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
5 years ago
here z=-w or -w^2 where w is complex root of unity as 1+w+w^2=0
they are asking (-w)^n that will be
=(-1)n-(-1)-n
=for n even it will become 0 and for n odd its also zero

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