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Math Help - Find the modulus

  1. #1
    Junior Member
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    Find the modulus

    I'm not sure how to deal with this problem (see attachment) when they have a treated as a real number. I know I have to use the modulus theorem but I think it may just be the algebra involved with leaving a as a real number that is giving me the problem. I have attached my working if it's not clear what I mean. (see attachment)

    Thanks, Daddy_Long_Legs
    Attached Thumbnails Attached Thumbnails Find the modulus-question-4.jpg   Find the modulus-question-4-working.jpg  
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  2. #2
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    You might note that \left| {2a - i} \right| = \left| {2a + i} \right| = \sqrt {4a^2  + 1} \;\& \;\left| {a + i} \right|^4  = \left( {a^2  + 1} \right)^2 .
    And so \left| z \right| = \frac{{\left( {a^2  + 1} \right)^2 }}<br />
{{\left( {\sqrt {4a^2  + 1} } \right)^7 }}.

    That may not be any better than what you have done.
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