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Math Help - complex analysis

  1. #1
    Amy
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    Question complex analysis

    I have 2 questions.

    Q1 In the following equation, by equating real and imaginary parts, find expressions for R6 and L in terms of R1, R2, R3, R4, R5 and C, given that the frequency is one radian per second.

    R1-j/ωC = R2+R3
    R4+R5 R6+jωL



    Thanks
    Attached Thumbnails Attached Thumbnails complex analysis-q2.jpg  
    Last edited by Amy; September 18th 2007 at 10:25 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Amy View Post
    I have 2 questions.

    Q1 In the following equation, by equating real and imaginary parts, find expressions for R6 and L in terms of R1, R2, R3, R4, R5 and C, given that the frequency is one radian per second.

    R1-j/ωC = R2+R3
    R4+R5 R6+jωL



    Thanks
    Lets assume that R_1, R_2, R_3, R_4, R_5, C \mbox{ and } L are all real and greater than zero, and that you mean:

    <br />
\frac{R_1-j/(\omega C)}{R_4+R_5}=\frac{R_2+R_3}{R_6+j \omega L}<br />

    if \omega=1 this becomes:

    <br />
\frac{R_1-j/ C}{R_4+R_5}=\frac{R_2+R_3}{R_6+j L}<br />

    Put R_4+R_5=R_{4,5} and R_2+R_3=R_{2,3}, then we have:

    <br />
\frac{R_1-j/ C}{R_{4,5}}=\frac{R_{2,3}}{R_6+j L}<br />

    and as none of the terms is zero flip this over to get:

    <br />
\frac{R_{4,5}}{R_1-j/ C}=\frac{R_6+j L}{R_{2,3}}<br />

    On the left multiply top and bottom by R_1+j/C and equate real and imaginary parts of both sides to get what you want.

    RonL
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