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Math Help - Simply Complex numbers

  1. #1
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    Simply Complex numbers

    Hey guys, was just given this question: Use the complex conjugate of z to find z^-1 when z equals 2+3i.

    Okay is it asking for the inverse of the complex number, or simply to multiple it by the power of -1?
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  2. #2
    Senior Member Peritus's Avatar
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    z^{ - 1}  = \frac{1}<br />
{z} = \frac{{z^* }}<br />
{{zz^* }} = \frac{{z^* }}<br />
{{|z|}}
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  3. #3
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    Hello, sanado!

    Use the complex conjugate of z to find z^{-1} when z \:=\:2+3i.

    We have: . z^{-1} \;=\;\frac{1}{2+3i}

    The conjugate of 2 + 3i is  2 - 3i


    Multiply top and bottom by the conjugate:

    . . \frac{1}{2+3i}\cdot\frac{2-3i}{2-3i} \;=\;\frac{2-3i}{4 -6i + 6i - (3i)^2} \;=\;\frac{2-3i}{13} \;=\;\frac{2}{13} - \frac{3}{13}i

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