Question 162617
Evaluate:
{{{i^17}}}
Recall that:
{{{i^1 = (sqrt(-1))^1}}}={{{i}}}
{{{i^2 = (sqrt(-1))^2}}}={{{-1}}}
{{{i^3 = (sqrt(-1))^3}}}={{{-1*i = -i}}}
{{{i^4 = (sqrt(-1))^4}}}={{{(-1)^2 = 1}}}
{{{i^5 = (sqrt(-1))^5}}}={{{1*i = i}}}
and so on...
So you can see that the sequence goes:
i, -1, -i, 1, i, -1, -1, 1,...as the exponent of i goes from:
1,  2,  3, 4, 5,  6,  7, 8,... every fourth power of i will be = 1, so if you divide the the given exponent of 17 (from {{{i^17}}}) by 4 you get 4 plus a remainder of 1, so {{{i^16 = 1}}}and{{{i^17 = i}}}