Inverse of complex number

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?

 

This does not itself have anything to do with "differential equations" so I am moving it to "general mathematics".

 

I think "supplement" is wrong. The reciprocal of 1 is 1, but the supplement of 0 is not 0.

 

Hey,
I think that arg(z^-1) = - arg (z)