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If z=e^((2pi i)/5), then 1+z+z^(2)+z^(3)...

If `z=e^((2pi i)/5)`, then `1+z+z^(2)+z^(3)+5z^(4)+4z^(5)+4z^(6)+4z^(7)+4z^(8)+5z^(9)=`

A

`0`

B

`4z^(3)`

C

`5z^(4)`

D

`-4z^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `(1+z+z^(2)+z^(3)+z^(4))+4z^(4)(1+z+z^(2)+z^(3)+z^(4))+5z^(9)`.
`=(1-z^(5))/(1-z)+4z^(4)((1-z^(5))/(1-z))+5z^(4)`
`=5z^(4)` `(:'z^(5)=1)`
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