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Thread: Absolute values and complex numbers

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    Cadet altSwift's Avatar
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    Absolute values and complex numbers

    question-cropped.png

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    In the answer to the question above on line 5 they seem to substitute an abs term inside of an abs term itself. A similar thing occurs on line 2,

    ie given that |x| = 1, |x - 2| can be written as |1 - 2|. However I thought that x = 1, -1, and so it can be written as either that or |-1-2|. Am I missing something here? I always thought that |x - y| cant be |x| - |y|. Thanks

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    Re: Absolute values and complex numbers

    On line 2 I think they are just taking the conjugate of the denominator, which doesn't matter because the absolute value function ignores the sign of the imaginary part.

    As stated in the justification, , so let and we have



    And because taking the conjugate is commutative with subtraction,



    On line 5, they seem to just be simplifying a term inside the absolute value function.



    I'm not sure why they wrote though.
    Last edited by fan96; 1 Feb 2018 at 9:02 PM.
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    HSC 2018 - [English Adv.] • [Maths Ext. 1] • [Maths Ext. 2] • [Chemistry] • [Software Design and Development]

    1(3√3) t2 dt cos(3π/9) = log(3√e) | Integral t2 dt, From 1 to the cube root of 3. Times the cosine, of three pi over nine, Equals log of the cube root of e.

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    Re: Absolute values and complex numbers

    that makes much mores sense now, I had to go back over the complex conjugate properties to wrap my head around it. Thanks!!
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