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Math Help - complex number simple (wrong thread)

  1. #1
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    complex number simple (wrong thread)

    hey guys ive got a problem

    If z = 3− i and w = 1+3i, evaluate Im (z∗w)/(2z − 3w) *=conjurate(ithink)

    wehn i expand the top line i get 10i/3-11i however it says the answer is 3/13??? ive tired multipling everything by 3+11i however im stuck. any help would be good. thanks
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by geffman1 View Post
    hey guys ive got a problem

    If z = 3− i and w = 1+3i, evaluate Im (z∗w)/(2z − 3w) *=conjurate(ithink)

    wehn i expand the top line i get 10i/3-11i however it says the answer is 3/13??? ive tired multipling everything by 3+11i however im stuck. any help would be good. thanks
    \frac {zw}{2z - 3w} = \frac {(3 - i)(1 + 3i)}{2(3 - i) - 3(1 + 3i)} = \frac {6 + 8i}{3 - 11i}

    now, multiply by \frac {3 + 11i}{3 + 11i}
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  3. #3
    Senior Member apcalculus's Avatar
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    If z = 3− i and w = 1+3i, evaluate Im (z∗w)/(2z − 3w) *=conjurate(ithink)
    z * w = (3-i)(1+3i) = 3 + 3 + 8i

    2z - 3w = 2(3-i) - 3(1+3i) = 6 - 2i - 3 -9i = 3 - 11i

    \frac{6+8i}{3 - 11i} =

    \frac{(6+8i)(3+11i)}{9+121} = \frac{18+88-42i}{130}\frac{106-42i}{130}

    Question: Does the 'Im' apply to the numerator only or the whole thing??
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    Quote Originally Posted by geffman1 View Post
    i expand the top line i get 10i/3-11i however it says the answer is 3/13??? ive tired multipling everything by 3+11i however im stuck. any help would be good. thanks
    You need to know that \text{Im} \left( {\overline z w} \right) = 10 there is no i in that.
    \text{Im}(z) is a real valued function.
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    i think it wants you to work out the whole thing, than just write what is the 'imaginary part'. thanks
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  6. #6
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    Quote Originally Posted by geffman1 View Post
    hey guys ive got a problem

    If z = 3− i and w = 1+3i, evaluate Im (z∗w)/(2z − 3w) *=conjurate(ithink)

    wehn i expand the top line i get 10i/3-11i however it says the answer is 3/13??? ive tired multipling everything by 3+11i however im stuck. any help would be good. thanks
    Ever saw "Cool Hand Luke"? "What we have here is a . . . "

    That star needs to be on top if you want it to be conjugate like z^* but even that is cheezy. Better to make a bar over it like \overline{z}. The \text{Im} and division operators are ambiguous. I would take \text{Im} having a higher precedence than division but that's not what you want. First get the answer in Mathematica. Yea, that's cheezy too but at least it eliminates the ambiguity in notation above. What we then have here is:

    \text{Im}\left(\frac{\overline{z} w}{2z-3w}\right)

    Edit: Make that times two.
    Last edited by shawsend; June 14th 2009 at 03:41 PM.
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