## rishabhjaiswal225499 one year ago if z is the non real fifth root of unity then the value of ^(l 1+z+z^2+z^-2+z^-1l)=?

1. rishabhjaiswal225499

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

2. goformit100

is it IIT question ?

3. rishabhjaiswal225499

yup

4. rishabhjaiswal225499

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

5. goformit100

6. hartnn

so you know how to solve it already

7. rishabhjaiswal225499

|dw:1389460828114:dw| what next

8. rishabhjaiswal225499

the options are 4,2,1,none

9. hartnn

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

10. hartnn

(????)/z^2

11. rishabhjaiswal225499

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

12. rishabhjaiswal225499

|dw:1389461100403:dw|

13. hartnn

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

14. hartnn

that gives one root as z=0

15. hartnn

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

16. hartnn

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

17. hartnn

so your entire numerator of the exponent goes to 0

18. hartnn

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

19. rishabhjaiswal225499

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

20. hartnn

oops

21. rishabhjaiswal225499

|dw:1389461448241:dw|

22. hartnn

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

23. rishabhjaiswal225499

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

24. hartnn

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