Question

The value of expression $i^{92}$ + $i^{93}$ + $i^{94}$ + $i^{95}$ is__

Answer 1

$i^{92}$ = $(i^4{)}^{23}$ = 1

$i^{93}$ = $i^{\left(4\right(23)+1)}$ = i

$i^{94}$ = $i^{\left(4\right(23)+3)}$ = $i^2$ = -1

$i^{95}$ = $i^{\left(4\right(23)+3)}$ = $i^3$ = -i

Hence, $i^{92}$ + $i^{93}$ + $i^{94}$ + $i^{95}$ =1+i-1-i=0

Note: Sum of 4 consecutive power of i is zero.

ie,$i^n$ + $i^{(n+1)}$ + $i^{(n+2)}$ + $i^{(n+3)}$ =0 , for n $ϵ$ Z