The smallest positive integral value of n such that [ 1+ 8 +i 8 1+ 8 -i 8 ]^n is purely imaginary, is equal to

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.