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Math Help - Complex Conjugate

  1. #1
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    Complex Conjugate

    I have seen other threads on this topic, but did not really understand them. They just seemed to sprawl off into nomenclature that I didn't follow, so I probably shouldn't actually be doing this, but hey.

    My question is, what is 1/(0.8-j1.6)?

    As far as I understood, it may be the same as z/z^2, although that may be only part way to representing it differently.
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  2. #2
    Super Member TheChaz's Avatar
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    How about an example, where I use i instead of j. We have the property that i^2 = -1.

    For example: \frac{1}{3 + 4i}

    Now the "complex conjugate" of 3 + 4i is 3 - 4i, so we multiply the numerator and denominator by this to get

    \frac{1}{3 + 4i} \times \frac{3 - 4i}{3 - 4i} = \frac{3 - 4i}{9 - 16i^2}

    And using what we know about i, this equals

    \frac{3 - 4i}{9 + 16} = \frac{3 - 4i}{25} = \frac{3}{25} - \frac{4}{25}i

    Did you mean \frac{\overline{z}}{z^2} ??
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  3. #3
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    Quote Originally Posted by AngusBurger View Post
    As far as I understood, it may be the same as z/z^2, although that may be only part way to representing it differently.
    You have incorrect notation: \dfrac{1}{z}=\dfrac{\overline{\,z\,}}{|z|^2}
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  4. #4
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    Sorry, that is what I meant.

    It's not as outrageous as I thought it would be, then. It's just Cartesian division (which is what I used to get the equation in the first place). Thank you for the clarification.
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