Question

Show that \[\frac{1}{1/z}=z\]for \(z\neq 0\)

Answer 1

I don't understand how I can show this?

\[\left(\left( x+iy \right)^{-1}\right)^{-1}\]

Answer 2

\[\left(\left( x+iy \right)^{-1}\right)^{-1}=x+iy=z\]

Answer 3

Put
\[
z=e^{ i \theta}\\
\frac 1 z = e^{- i \theta}\\
\frac{1}{\frac 1 z}= \frac 1{e^{-i \theta}}=e^{i\theta}=z

\]

Answer 4

ok. why do I have to do it in exponential form though?

Answer 5

The inverse of an inverse of a non zero complex number is the number itself

Answer 6

You do not need to. That is another way of seeing it

Answer 7

oh ok. just wasn't sure if this was a trick question or something? thanks.