Question 14062
note {{{i^83}}}={{{i^80*i^3}}}.
we have {{{i^80 * (-i)}}} since i^3 = -i.
and {{{i^80}}}={{{(i^2)^40}}}.
we know {{{i^2}}} = -1.
so what we have  {{{(-1)^40 * (-i)}}}.
we know {{{(-1)^evenpower}}}=1
and {{{(-1)^oddpower}}}= -1.
since 40 is even {{{(-1)^40}}} = 1
so we have {{{1*(-i)}}} = -i.
Hope this helps you again.