Which of the following is equivalent to the complex number i^8?
2 answers:
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If we use the substitution 
, then 
. If you try substituting just 
and 
into the integrand, though, you'll notice that there's a 
left over that we have to deal with.
To get rid of this problem, use the identity
and substitute in the left side of the identity for the extra , as shown:
From there, we can substitute in and , and then evaluate:
To get rid of this problem, use the identity
From there, we can substitute in