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Math Help - complex numbers

  1. #1
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    complex numbers



    z1=4.5e^o.5j
    z2=3+j
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  2. #2
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    Quote Originally Posted by cheesepie


    z1=4.5e^o.5j
    z2=3+j
    The first thing to do is to convert z1 into a + bj form:
    z_1 = 4.5(cos(0.5) + j sin(0.5)) \approx 3.9491 + 2.1574 \, j

    Now consider:
    \frac{1}{\frac{1}{z_1} + \frac{1}{z_2}}

     = \frac{1}{\frac{1}{z_1} + \frac{1}{z_2}} \cdot \frac{z_1z_2}{z_1z_2}

     = \frac{z_1z_2}{\frac{1}{z_1} \cdot (z_1z_2) + \frac{1}{z_2} \cdot (z_1z_2)}

     = \frac{z_1z_2}{z_2 + z_1}

    So insert your expressions for z1 and z2 into this and there's your answer.

    Warning! You will need to rationalize the denominator before you are done!

    -Dan
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  3. #3
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    z_1 \,=\,4.5e^{0.5}\qquad z_2\,=\,3+j
    Typo the first should read:

    <br />
z_1 =4.5e^{0.5\ \bold{j}}<br />

    RonL
    Last edited by CaptainBlack; August 16th 2006 at 04:49 AM.
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