If `omega`is an imaginary fifth root of unity, then find the value of `loe_2|1+omega+omega^2+omega^3-1//omega|dot`

If `omega`is an imaginary fifth root of unity, then find the value of

1.	If `omega`is an imaginary fifth root of unity, then find the value of `loe_2\|1+omega+omega^2+omega^3-1//omega\|dot`
Answer» Here, `omega^(5)=1.` Therefore, `omega^(-1)=omega^(4)` Also, `1+omega+omega^(2)+omega^(3)+omega^(4)=0` `:." "log_(2)\|1+omega+omega^(2)+omega^(3)-(1)/(omega)\|` `=log_(2)\|1+omega+omega^(2)+omega^(3)-omega^(4)\|` `=log_(2)\|-2omega^(4)\|=log_(2)2=1" "(because\|omega\|=1)`

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If `omega`is an imaginary fifth root of unity, then find the value of `loe_2|1+omega+omega^2+omega^3-1//omega|dot`

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