Inverse of complex number

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  • #1
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Main Question or Discussion Point

How does taking the multiplicative inverse (reciprocal) of a complex number change its magnitude and argument?
 

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  • #2
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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?
 
  • #3
HallsofIvy
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This does not itself have anything to do with "differential equations" so I am moving it to "general mathematics".
 
  • #4
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I think "supplement" is wrong. The reciprocal of 1 is 1, but the supplement of 0 is not 0.
 
  • #5
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Hey,
I think that arg(z^-1) = - arg (z)
 

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