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Math Help - Complex number question

  1. #1
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    Complex number question

    Hey,

    I'm new as you can probably tell, so hello everyone! I'm doing AS Further Mathematics as an extra AS level during my second year at college, and I am finding it difficult to answer the following question in my homework:

    Find the complex number z which satisfies (2+i)z+(3-2i)z^*=32 .

    How would I go about attempting this? I'm unsure of what step/s to take first.

    Thanks very much for any help!
    Last edited by Fandango1992; March 26th 2010 at 02:36 AM.
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  2. #2
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    Hi

    Quote Originally Posted by Fandango1992 View Post
    Find the complex number z which satisfies (2+i)z+(3-2i)z^*
    The question is not complete : which satisfies what ?
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  3. #3
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    Quote Originally Posted by running-gag View Post
    Hi



    The question is not complete : which satisfies what ?
    Oops, sorry! I have recorrected it. Must've been shattered...
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  4. #4
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    z* is the complex conjugate of z?

    Let z= x+ iy. Then your equation is (2+i)(x+ iy)+(3-2i)(x- iy)=32. Multiplying that out, 2x- y+ i(x+ 2y)+ 3x- 2y+ i(-2x- 3y)= 32. Set the real part of the left side equal to 32 and the imaginary part equal to 0. You will have two equations to solve for x and y.
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  5. #5
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    Just for fun you can solve it another way
    (2+i)z+(3-2i) \bar{z}=32

    Take the conjugate of both sides
    (2-i)\bar{z}+(3+2i) z=32

    This leads to the following system
    (2+i)z+(3-2i) \bar{z}=32
    (3+2i) z + (2-i)\bar{z}=32
    that you can solve for z by eliminating \bar{z}
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  6. #6
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    Thanks a lot for your help! Now I can move to question two, haha. Good times...
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