Question
The smallest positive integral value of n such that [ 1+ 8 +i 8 1+ 8 -i 8 ]^n is purely imaginary, is equal to
BITSAT
Mathematics
Complex Number
2022
BITSAT 2022
BITSAT Mathematics Question (2022) — Solution
Options
- A. 4
- B. 3
- C. 2
- D. 8
Answer
A. 4
Step-by-step solution
[ 1+ 8 +i 8 1+ 8 -i 8 ]^n= [ 1+ +i 1+ -i ]^n [ = 2 - 8 ] = [ 2 ^2 2 +2 i 2 2 2 ^2 2 -2 i 2 2 ]^n = [ 2 +i 2 2 -i 2 ]_ - ^n= (e^ 2 i 2 ]^n=e^ i n =e^ i n ( 3 8 ) = 3 n 8 +i 3 n 8 For n=4 we get imaginary part.
Related: Mathematics — Complex Number · All PYQ Banks