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Math Help - module question

  1. #1
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    module question

    http://i34.tinypic.com/juakhy.jpg

    i know that the module of a complex number is the square root
    of the real and complex coefficients

    but here i cant see that they done it that way
    ?
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  2. #2
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    Quote Originally Posted by transgalactic View Post
    http://i34.tinypic.com/juakhy.jpg

    i know that the module of a complex number is the square root
    of the real and complex coefficients

    but here i cant see that they done it that way
    ?
    It is important to note what |z - i|^2 and |z + i|^2 represent.

    The represent circles in the complex plane. You are trying to find where the circles overlap.



    I would convert it to real and imaginary parts...

    Let z = x + iy.


    Therefore

    |z - i|^2 = |z + i|^2

    |x + iy - i|^2 = |x + iy + i|^2

    |x + i(y - 1)|^2 = |x + i(y + 1)|^2

    x^2 + (y - 1)^2 = x^2 + (y + 1)^2

    (y - 1)^2 = (y + 1)^2

    y^2 - 2y + 1 = y^2 + 2y + 1

    -2y = 2y

    0 = 4y

    y = 0.


    So it is telling you that the two circles will overlap on the x-axis.
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  3. #3
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    wow you got the correct answer in another way

    thanks
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  4. #4
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    Quote Originally Posted by transgalactic View Post
    http://i34.tinypic.com/juakhy.jpg

    i know that the module of a complex number is the square root
    of the real and complex coefficients
    The modulus of a complex number is the square root of the sum of the squares of the real and complex coefficients.

    but here i cant see that they done it that way
    ?
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