Question 45882
You can work this out for yourself:

{{{i = sqrt(-1)}}} = i
{{{i^2 = (sqrt(-1))^2}}} = -1
{{{i^3 = -1sqrt(-1)}}} = {{{-1*i}}} = -i
{{{i^4 = (i^2)^2}}} = {{{(-1)^2 = 1}}}
{{{i^5 = (i^4)*i}}} = i

As you can see, {{{i^n}}} goes around in circles, starting with i when n = 1...as follows.

n = 1..{{{i^1 = i}}}
n = 2..{{{i^2 = -1}}}
n = 3..{{{i^3 = -i}}}
n = 4..{{{i^4 = 1}}}
n = 5..{{{i^5 = i}}} now we're back to where we started.

So to find the value of {{{i^34}}}, you divide 34 by 4 and then take the remainder (it's 2 in this case) and find {{{i^2}}} from the above table.

{{{i^34 = -1}}}