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its find the value of 2^(l1+z+z^2+z^-2-z^-1l) sry i wrote it wrong

is it IIT question ?

yup

you can use z+z^2+z^3+z^4=0 for z=fifth root of unity

Show your working.

so you know how to solve it already

|dw:1389460828114:dw|
what next

the options are 4,2,1,none

simplify this
1+z+z^2+z^-2+z^-1

(????)/z^2

i did it by taking the denominator
|dw:1389461042399:dw|

|dw:1389461100403:dw|

z+z^2+z^3+z^4=0
is incorrect

that gives one root as z=0

z^5 =1
z^5 -1^5 = 0

(z-1)(1+z+z^2+z^3+z^4) = 0
as z not = 1
(1+z+z^2+z^3+z^4) = 0

so your entire numerator of the exponent goes to 0

did u follow ?
if yes, i think, you'll get the answer now :)

no u didnt saw that i corrected the question its 1-z+z^2+z^3+z^4
and not 1+z+z^2+z^3+z^4

oops

|dw:1389461448241:dw|

then i should say, there's typing error in the question
OR
the answer is NONE

yup i also thought so thanks for your time by the way

because z is complex, so will be 2^(-2/z)
welcome ^_^