Question 361631
{{{i^40}}} is a problem in its self {{{i^40=0}}} the reason why i say this is because my teacher taught us a method to use for degree of i...here it is:

ex: Evaluate {{{i^533}}}
    {{{533/4=133+1/4}}} 533 divided by 4 = 133 R(1)

Now this tells you That the Remainder is 1, Use that with this chart:
               {{{i^0=0}}}
               {{{i=sqrt(i)=i}}}
               {{{i^2=-1}}}
               {{{i^3=i}}}
               {{{i^4=-1}}}
As you can see ; Odd degree numbers =i and even degree numbers= -1. 


NOW HERE IS YOUR PROBLEM WORKED OUT:
{{{i^40}}}
{{{40/10=4}}} See No remainder so you would have degree 0, then plug it into chart and the answer is 0.


Hope this has helped you out.