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Math Help - complex numbers

  1. #1
    Junior Member
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    complex numbers

    the question is:
    write each of the following in the form x+yi, wherre x and y are real numbers:

    i^12+i^15

    as my for i^12 i get 1 but for i^15 im not sure i think its -1 (ixi)

    and can you please answear i^7-i^11 - dont anderstand the answear, how they both=0


    thnx
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  2. #2
    MHF Contributor

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    Powers of i are "periodic with period 4". That is, i^0= 1, i^1= i, i^2= -1, i^3= (i^2)(i)= -i, and i^4= (i^2)(i^2)= (-1)(-1)= 1 and now everything repeasts.

    4 divides into 15 3 times with remainder 3: 3(4)+ 3= 12+ 3= 15. That means that i^{15}= i^{4+ 4+ 4+ 3}= i^4(i^4)(i^4)(i^3)= 1(1)(1)(i^3)= i^3= -i.

    7= 4+ 3 and 11= 4+ 4+ 3 so i^7= (1)i^3= -i and i^{11}= (1)(1)(i^3)= -i. They don't "both = 0". They both equal -i so their difference is 0.
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