madmerc
  • madmerc
Simplify i^31 1 -1 -i i
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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freckles
  • freckles
i^4=1 so try dividing 31 by 4 and we will see what is left over when you do 31/4, don't do decimal style, do remainder style
madmerc
  • madmerc
7.75 ? what is remainder style
freckles
  • freckles
so I guess you never did mix fractions then?

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madmerc
  • madmerc
wait is it like 7 and 3/4
freckles
  • freckles
|dw:1446394929516:dw|
madmerc
  • madmerc
so 3?
freckles
  • freckles
yes very good 31-28 is 3 3 is what is left over 3 is the remeinder
freckles
  • freckles
remainder *
freckles
  • freckles
\[i^{31}=i^{4(7)+3}=(i^4)^7 i^3=?\]
freckles
  • freckles
since i^4=1 and 1^7=1 then all you really have to compute is i^3
madmerc
  • madmerc
I still don't understand how to do that
freckles
  • freckles
do you know law of exponents?
madmerc
  • madmerc
isn't i^3 = -i
freckles
  • freckles
yes because i^3 is i^2*i=(-1)*i=-i
madmerc
  • madmerc
so the answer to i^31 is -i ?
freckles
  • freckles
yes we just found that above...
madmerc
  • madmerc
thanks

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