Manipal MET2014MathematicsComplex Number
If 1, , ^2, ^ n-1 are n, n^ th roots of unity, then the value of (9- ) (9- ^2 ) (9- ^3 ) (9- ^ n-1 ) will be
Options
- A9^n+1 8
- B9^n-1
- C9^n-1 8
- D9^n+1
Correct answer
C. 9^n-1 8
Step-by-step solution
aligned & Let x=(1)^ 1 / n & x^n-1=0 & or x^n-1=(x-1)(x- ) (x- ^2 ) (x- ^ n-1 ) & x^n-1 x-1 =(x- ) (x- ^2 ) (x- ^3 ) aligned Putting x=9 on both sides, we get (9- ) (9- ^2 ) (9- ^3 ) (9- ^ n-1 )= 9^n-1 8