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Math Help - Complex number question

  1. #1
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    Complex number question

    Find Z1 and Z2 , given that:

    (1 + i )Z1 + Z2 = 1 + i
    4Z1 + (1 - i)Z2 = 4+ 2i

    I tried to solve by letting Z1 = a + bi and Z2 = c + di and comparing coefficients with the Cartesian form on the right hand side of the equation. I cant get the answer as solving four unknowns seems a bit too much for me, is there any simpler way to solve this??
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  2. #2
    MHF Contributor red_dog's Avatar
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    \left\{\begin{array}{l}(1+i)z_1+z_2=1+i\\4z_1+(1-i)z_2=4+2i\end{array}\right.

    Multiply the first equation with 4 and the second with -(1+i). Then add the equations:

    2z_2=2-2i\Rightarrow z_2=1-i

    Plug z_2 in the second equation:

    4z_1=4+4i\Rightarrow z_1=1+i
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  3. #3
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    Thanks! I got an idea similar as yours earlier but still cant get it to work, now i know why. what i was think about just now is letting z1 = ( 1 - i) and letting z2 = (1+i), obviously that is the wrong substitution. Thanks again!
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  4. #4
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    On the other hand, if you multiply the first equation by 1-i we get 2z_1+(1-i)z_2=2.
    Now substract that from the second equation.
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