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Inverse of complex number

  1. Mar 9, 2010 #1
    How does taking the multiplicative inverse (reciprocal) of a complex number change its magnitude and argument?
  2. jcsd
  3. Mar 9, 2010 #2
    A complex number z, when inverted, will have its magnitude also inverted, [tex]|z^{-1}| = \frac{1}{|z|}[/tex] and its argument will become its supplement, [tex]arg(z^{-1}) = \pi - arg(z)[/tex]

    Why don't you try proving that?
  4. Mar 10, 2010 #3


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    This does not itself have anything to do with "differential equations" so I am moving it to "general mathematics".
  5. Mar 10, 2010 #4
    I think "supplement" is wrong. The reciprocal of 1 is 1, but the supplement of 0 is not 0.
  6. Mar 11, 2010 #5
    I think that arg(z^-1) = - arg (z)
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