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Simplify

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simplify i^-23 and i^2015
asked Dec 24, 2017 in PRECALCULUS by anonymous

1 Answer

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Note ;

i   =   i

i^2   =   -1

i^3   =   - i

i^4   =   1

 

a)   i^-23

Consider

i^23   =   (i^20) (i^3)

         =   [ (i^4)^5 ]  (-i)

         =   [ (1)^5 ]  (-i)

         =   (1)  (-i)

I^ 23 =   - i

i^-23   =   1/(i^23)

             =   1/(-i)  (i/i)

             =   i / -(i^2)

             =   i / -(-1)

i^-23   =   i

b)

i^2015   =   (i^2012)(i^3)

                 =   [(i^4)^503](-i)

                 =   [(1)^503](-i)

i^2015   =   - i

answered Dec 24, 2017 by homeworkhelp Mentor

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