Question 79349
{{{i^1= i}}}        {{{ i^5 = i}}}
{{{i^2= -1 }}}      {{{ i^6 = -1}}}
{{{i^3= -i }}}      {{{  i^7= -i}}}
{{{i^4= 1 }}}       {{{ i^8 = 1}}}
The easiest property to make use of is
{{{i^4= 1 }}} because every time you 
multiply it times itself, you still get 1
{{{i^4 * i^4 = 1}}}
{{{i^4 * i^4 * i^4 = 1}}}
{{{i^4 * i^4 * i^4 * i^4 = 1}}}
Remember you ADD the exponents in each case, so
{{{i^8 = 1}}}
{{{i^12 = 1}}}
{{{1^16 = 1}}}
Think of {{{i^65}}} as {{{i^4}}} multiplied times itself a certain
number of times and multiply that by whatever factor is left over
{{{65/4 = 16}}} and 1 remainder
What you've got is {{{(i^4)^16 * i}}} or
{{{1^16 * i = i}}}
So, {{{i^65 = i}}} answer