Most Important Selected Qs for JEE AdvancedMathematicsComplex Number
Paragraph Roots of z^n-1=0 are 1, , ^2, ^3, . . ^ n-1 where = 2 n +i 2 n so z^n-1=(z-1)(z- ) ( z - ^ n -1 ) On the basis of above information, answer the following questions : Question If n =5 , then (1+ ) (1+ ^2 ) (1+ ^3 ) (1+ ^4 ) is equal to -
Options
- Azero
- B-1
- C1
- D2
Correct answer
C. 1
Step-by-step solution
aligned & n =5, ^5=1 & and 1+ + ^2+ ^3+ ^4=0 & (1+ ) (1+ ^2 ) (1+ ^3 ) (1+ ^4 ) & = (1+ + ^2+ ^3 ) (1+ ^3+ ^4+ ^7 ) & = (- ^4 ) (1+ ^2+ ^3+ ^4 ) & = (- ^4 )(- )= ^5=1 aligned