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Math Help - transpose formula

  1. #1
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    transpose formula

    Hello.

    I'm stuck with transposing a formula.

    D = real(pr) / sqrt( real(pr)^2 + imag(pr)^2)

    If I know D and Imag(pr) how do I find Real(pr)?

    Many thanks

    Albert
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  2. #2
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    D = real(pr) / sqrt( real(pr)^2 + imag(pr)^2)

    Multiply both sides by the denominator of the right side:

    d (sqrt( real(pr)^2 + imag(pr)^2) = real(pr)

    Square both sides:

    d^2 * (real(pr)^2 + imag(pr)^2) = real(pr)^2

    Distribute:

    d^2 * real(pr)^2 + d^2 * imag(pr)^2 = real(pr)^2

    Regroup:

    d^2 * real(pr)^2 - real(pr)^2 = -d^2 * imag(pr)^2

    Factor:

    real(pr)^2 (d^2 - 1) = -d^2 * imag(pr)^2

    Divide by (d^2 - 1):

    real(pr)^2 = (-d^2 * imag(pr)^2) / (d^2 - 1)

    Sqrt both sides:

    real(pr) = +/- sqrt[ (-d^2 * imag(pr)^2) / (d^2 - 1) ]


    Algebra 1 really.
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  3. #3
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    Thank you very much. That's great.

    Best regards

    Albert
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