Question 361631
{{{i^n}}} cycles in factors of 4
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{{{i^0=1}}}
{{{i^1=i=sqrt(-1)}}}
{{{i^2=-1}}}
{{{i^3=i^2*i=-1*i=-i}}}
{{{i^4=i^2*i^2=-1*-1=1=i^0}}}
{{{i^5=i^4*i=i=i^1}}}
and as you can see values recycle based on xmod(4) (ie the remainder of dividing by 4)

So since you want to know {{{i^40}}} and since 40mod(4)=0 then 
{{{i^40=i^0=1}}}