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    The question and what I've done so far:

    http://i1352.photobucket.com/albums/...psb591132c.jpg

    The blue bit is from the mark scheme - but I don't understand how they have come to this
    And the red bits are 'rules' we can use for modulus

    I've written out the complex and the complex conjugate but not sure what to do!
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    Well first, sub in z= r ( cosθ + i sinθ ) into the modulus. Then simply take the modulus of the thing which is root of real part squared plus imaginary part squared (the root goes away because the modulus is squared in the question) . So your real part is rcosθ + 1 and imaginary part is -rsinθ. Then just expand the brackets.
    This is the same as finding the modulus of eg : 3 + 2i. you would do
    √ 3^2 + 2^2. you are doing the same thing here
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    use the last rule to begin with, i.e |1-z|^{2}=(1-z)(1-\bar{z})

    (since the conjugate of 1-z is 1-\bar{z})

    expand that top line,
    replace the ( z z bar) with mod z squared,
    then sub in the polar forms and you should get the result
 
 
 
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