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Math Help - complex numbers

  1. #1
    Member u2_wa's Avatar
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    complex numbers

    when does this relation holds?
    [z1]-[z2]=[z1+z2] ; [z1] & [z2] represents the modulus of two complex numbers.
    to me only when z2=0?
    is there any other possibility?
    Last edited by u2_wa; February 11th 2009 at 07:32 AM.
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  2. #2
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    Quote Originally Posted by u2_wa View Post
    when does this relation holds?
    [z1]-[z2]=[z1+z2]
    to me only when z2=0?
    is there any other possibility?
    [z1]-[z2]=[z1+z2]

    let's say

    z1=any integer(e.g let say 2)

    z2=0

    2-0=0+2

    2=2

    make sense.. i don't think there's any more possibility for other values other than zero
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  3. #3
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    There are other possibilities

    z_1 = \alpha \: e^{i\theta} and z_2 = \beta \: e^{i(\theta+\pi)} = - \beta \: e^{i\theta} with \alpha \geq \beta \geq 0

    Then
    |z_1| = \alpha and |z_2| = \beta

    z_1 + z_2 = (\alpha - \beta) \: e^{i\theta}

    |z_1 + z_2| = \alpha - \beta = |z_1| - |z_2|

    For instance
    |2i + (-i)| = |i| = 1 = |2i| - |-i|
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  4. #4
    Member u2_wa's Avatar
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    Thumbs up

    Quote Originally Posted by running-gag View Post
    There are other possibilities

    z_1 = \alpha \: e^{i\theta} and z_2 = \beta \: e^{i(\theta+\pi)} = - \beta \: e^{i\theta} with \alpha \geq \beta \geq 0

    Then
    |z_1| = \alpha and |z_2| = \beta

    z_1 + z_2 = (\alpha - \beta) \: e^{i\theta}

    |z_1 + z_2| = \alpha - \beta = |z_1| - |z_2|

    For instance
    |2i + (-i)| = |i| = 1 = |2i| - |-i|
    Thanks for it. Can you please give me graphical proof for it!
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  5. #5
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    Here it is

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