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Math Help - Simplifying complex numbers?

  1. #1
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    Simplifying complex numbers?

    Can anyone show me how to simplify

    2- square root 2i divided by 3+square root 6i

    Now I used the conjugate 3- square root 6i

    On the numerator I end up getting -6-2 square root 6- 3 square root 2i

    On the denominator I end up getting 27

    However I checked my answer and apparently I am wrong

    What error could I have committed?
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  2. #2
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    Quote Originally Posted by homeylova223 View Post
    Can anyone show me how to simplify
    2- square root 2i divided by 3+square root 6i
    Now I used the conjugate 3- square root 6i
    On the numerator I end up getting -6-2 square root 6- 3 square root 2i
    On the denominator I end up getting 27
    The denominator should be 15. It is square of the absolute value of the denominator.
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  3. #3
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    So would the conjugate be 3+square root 6i and multiply this to the denominator to get it squared?
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  4. #4
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    Z = 3 + i \sqrt{6} when conjugated you get 3 - i \sqrt{6} ....

    so denominator looks like 3^2 + 6 = 15
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  5. #5
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    Quote Originally Posted by homeylova223 View Post
    So would the conjugate be 3+square root 6i and multiply this to the denominator to get it squared?
    This is a of the most use formula.
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  6. #6
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    I squared it

    and I end up getting

    9+3\sqrt{6i} + 3\sqrt{6i} + 36i^2

    How do you get 15 as the denominator?
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  7. #7
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    Quote Originally Posted by homeylova223 View Post
    Can anyone show me how to simplify

    2- square root 2i divided by 3+square root 6i

    Now I used the conjugate 3- square root 6i
    I assume that by "used" you mean you multiplied both numerator and denominator by it. Okay, (2- i sqrt(2))(3- i sqrt(6))= 2(3)- 2(i sqrt(6))- (i sqrt(2)(3)+ i^2(sqrt(2)(sqrt(6)= 6- 2i sqrt(6)- 3i sqrt(2)- sqrt(12)- not at all what you have.
    (3+ i sqrt(6))(3- i sqrt(6)= 9- i^2(sqrt(6))^2= 9+ 6= 15.

    On the numerator I end up getting -6-2 square root 6- 3 square root 2i

    On the denominator I end up getting 27

    However I checked my answer and apparently I am wrong

    What error could I have committed?
    Since you don't show what you did- exactly how you multiplied, it is impossible to say. I do note that 27 = 36 - 9 so you might have squared 6 instead of sqrt(6)- but then I can't see why you would have subtracted.
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  8. #8
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    Quote Originally Posted by homeylova223 View Post
    I squared it

    and I end up getting

    9+3\sqrt{6i} + 3\sqrt{6i} + 36i^2

    How do you get 15 as the denominator?
    Careful with the negative signs. The denominator is


    -Dan
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