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Math Help - imaginary number

  1. #1
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    imaginary number

    if 1^2 = -1 then what does i^5+i^6+i^7= anyone give me somewhere to start on this one
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  2. #2
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    I'm sure it was just a typo, but it should be  i^2 = -1 . To compute  i^5 + i^6 + i^7 just calculate what  i^5 is, what  i^6 is and what  i^7 is, then add them together.

    For example, you know that  i^2 = -1 , so  i^3 = i^2*i = -i . Continuing on,  i^4 = i^3 * i = -i*i = -i^2 = 1 and continue in this process.
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  3. #3
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    A simple but interesting result which we obtain from above is that :

    The sum of any 4 consecutive powers of i is equal to zero.

    Hence using this result,

     i^5+i^6+i^7+i^8=0

    Hence the value of the given expression is merely -i^8

    i.e. =  -i^8

    and we know, i^4=1

    Hence the required answer is -1
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  4. #4
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    so how do we know that i^4 = 1 and why then would -i^8 = -1
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  5. #5
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    since i^2= -1

    Square both sides,

    i^4=1

    Now, square both sides again,

    i^8=1

    so clearly -i^8=-1
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  6. #6
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    ok thanks again for your patience
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