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Math Help - simplifying nasty complex math expression

  1. #1
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    simplifying nasty complex math expression

    \frac{4+3j}{200}(\frac{-3+4j}{25})^n+\frac{4-3j}{200}(\frac{-3-4j}{25})^n

    I know 100% that this expression must be real since the excitation to the system was real in my Linear, time-invariant system of differential equations.

    Somehow, the solutions manual transforms the equation into some e^(jw)s, and uses Euler's identity from there to reach two real sinusoidal functions. The problem I'm having is making the e^(jw) out of that expression in the first place.
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  2. #2
    A Plied Mathematician
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    Ok, you have some exponentiation going on there, twice. What I would do is convert the rectangular representations you have into polar ones via the following: if you have

    z=x+jy, then

    z=r\,e^{j\theta}, where

    r=\sqrt{x^{2}+y^{2}}, and

    \theta=\tan^{-1}\!\left(\frac{y}{x}\right).

    Exponentiation, and multiplication for that matter, is easier in the polar representation of complex numbers than in the rectangular. However, I would definitely use rectangular for addition and subtraction. So, I would get those numbers into polar, do the exponentiation, convert back to rectangular, and see what you get.
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  3. #3
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    ahhh, of course. Thanks.
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  4. #4
    A Plied Mathematician
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    No problem. Have fun!
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