Question 221204
simplify imaginary i^33
as much as possible


Step 1. Since {{{i=sqrt(-1)}}}, then {{{i^2=sqrt^2(-1)=-1}}}.  Also, {{{i^3=-i}}} and {{{i^4=1}}}


Step 2. Therefore {{{i^33=(i^4)^8*i=1^8*i=i}}}  where  {{{(i^4)^8=i^32}}}.


Step 3.  ANSWER:  {{{i^33=i}}}


I hope the above steps were helpful. 


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Dr J


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