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If z+1/z=2cos6^@ , then z^1000+1/[z^1000...

If `z+1/z=2cos6^@` , then `z^1000+1/[z^1000]` +1 is equal to

A

`0`

B

`1`

C

`-1`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `z+(1)/(z)=2cos6^(@)`
`:.z=cos6^(@)+-isin6^(@)`
`impliesz^(1000)+(1)/(z^(1000))+1=2cos6000^(@)+1=2xx(-(1)/(2))+1=0`
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