99 Percentile Qs Bank for JEE MainMathematicsComplex Number
_ k=1 ^6 [ 2 k 7 -i 2 k 7 ] is equal to
Options
- A-1
- B0
- C-i
- Di
Correct answer
D. i
Step-by-step solution
We have, _ k=1 ^6 [ 2 k 7 -i 2 k 7 ] aligned & = _ k=1 ^6 [(-i) ( 2 k 7 +i 2 k 7 ) ] & =(-i) _ k=1 ^6 ( 2 k 7 +i 2 k 7 )=(-i) _ k=1 ^6 ^k aligned Let = 2 k 7 +i 2 k 7 =(-i) ( + ^2+ ^3+ + ^5 ) Here, + ^2+ ^3+ + ^6 follows G.P. so its sum. S = (1- ^6 ) 1- = - ^7 1- = -1 1- =i [ ^7= 2 +i 2 =1 ] Thus, =-i(-1) =i