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Math Help - Finding real numbers in equations containing complex numbers

  1. #1
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    Finding real numbers in equations containing complex numbers

    Ok, teacher gave us a quick exercise overnight, to help with tomorrow's work. Was 2 parts, I've done the first and I'm sure it's right, I just have no clue where to start the second.

    A) Find the real numbers p and q where :

    p+q+i(p-q) = 4+2i

    So, we know i(p-q) has to be the +2i part, and p+q has to be 4 -

    p - q = 2 and p + q = 4

    p=4-q

    4-2q=2

    q=1.

    P+1=4

    p=3

    The second one is -

    2(p+iq)=q-ip-2(1-i)

    Now, I've scribbled out a lot so far. I started by expanding all the brackets, leaving -

    2p+2iq=q-ip-2-2i

    Which has no like terms at all. So I tried re-arranging to get p on it's own -

    2p=q-ip-2-2i-2iq

    p= \frac{q-ip-2-2i-2iq}{2}

    But that just makes me even more confused. Anyone know if I'm on the right path?
    Last edited by mash; March 4th 2012 at 11:16 AM. Reason: fixed latex
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  2. #2
    Junior Member
    Joined
    Sep 2010
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    You should think in terms of real part and imaginary part.
    so simplify it to p(2+i) + q(2i-1) = -2+2i
    real part is equal to -2
    so Re (-2 + 2i) = -2 = 2p -q
    and Im (-2 + 2i) = 2 = p + 2q.
    from there u should be able to solve it by breaking out for example p in both equations and solve for q and then for p.
    u will get that q is 1.2 and p is -0.4.
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