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Math Help - Simplify i

  1. #1
    Junior Member fluffy_penguin's Avatar
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    Simplify i



    = (i^3)^7
    =-i

    Also can someone help me fill in my i chart that my teacher started...

    i^1 = ?
    i^2 = -1
    i^3 = i^2 * i = -i
    i^4 = i^2 * i^2 = 1
    i^5 = i^4 * i = i
    i^6 = i^3 * i^3= ?
    i^7 = i^4 * i^3= ?
    i^8 = i^4 * i^4= ?
    i^9 = i^5 * i^4= ?
    i^10 = i^5 * i^5= ?
    i^11 = i^5 * i^6= ?
    i^12 = i^5 * i^7= ?
    i^13 = i^5 * i^8= ?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by fluffy_penguin View Post


    = (i^3)^7
    =-i
    that's incorrect i^{21} = i \cdot i^{20} = i \cdot \left( i^2 \right)^{10} = i

    see here, they have a nice list of rules, it will also help you check the answers for your chart
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Also can someone help me fill in my i chart that my teacher started...

    i^1 = ?
    i^2 = -1
    i^3 = i^2 * i = -i
    i^4 = i^2 * i^2 = 1
    i^5 = i^4 * i = i
    i^6 = i^3 * i^3= ?
    i^7 = i^4 * i^3= ?
    i^8 = i^4 * i^4= ?
    i^9 = i^5 * i^4= ?
    i^10 = i^5 * i^5= ?
    i^11 = i^5 * i^6= ?
    i^12 = i^5 * i^7= ?
    i^13 = i^5 * i^8= ?
    just reuse the previous values.

    for instance, i^6 = i^3 \cdot i^3

    so look up in your chart for i^3, we see that i^3 = -i

    thus, i^6 = i^3 \cdot i^3 = -i \cdot -i = i^2 = -1


    continue the same way. and use the link i gave you to check your answers
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  4. #4
    Junior Member fluffy_penguin's Avatar
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    Thanks.
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  5. #5
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    Hello, fluffy_penguin!

    Can someone help me fill in my chart that my teacher started...

    \begin{array}{ccccccc}i^1 & = & & & & &{\color{blue}i} \\i^2 & = & & & & & {\color{blue}\text{-}1} \\i^3 & =&  \;\,i^2\cdot i \;&= & (\text{-}1)i &=& {\color{blue}\text{-}i} \\i^4 &=& \;\,i^3\cdot i \;& = & (\text{-}i)(i) &=& {\color{blue}1}\end{array}
    \begin{array}{ccccccc}i^5 &=& i^4\cdot i &=& (1)(i)& = & {\color{red}i} \\i^6 &=& i^5\cdot i &=& (i)(i ) &=& {\color{red}\text{-}1} \\i^7 &=& (i^6)(i) &=&(\text{-}1)(i) &=& {\color{red}\text{-}i} \\i^8 &=& (i^7)(i) &=& (\text{-}i)(i) &=& {\color{red}1}\end{array}
    Don't you see the pattern?

    The successive powers are: . i,\;-1,\;-i,\;1 . . . . . over and over.



    Simplify: . i^{21}
    We know that: . i^4 \,=\,1

    So we have: . i^{21} \:=\:i^{20}\cdot i \;=\;(i^4)^5\cdot i \;=\;(1)^5\cdot i \;=\;i

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