The multiplicative inverse of $z$ is

\frac{z}{| z |^{2}}

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\frac{¯ ¯ ¯ z}{| z |^{2}}

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\frac{¯ ¯ ¯ z}{| z |}

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\frac{^{2}}{| z |}

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Solution

The correct option is C $\frac{¯ ¯ ¯ z}{| z |^{2}}$
Let
$z = r e^{i θ}$
Let $T$ be the multiplicative inverse of $z$ .
Then
$z . T = 1$
Or
$r e^{i θ} . T = 1$
Or
$T = \frac{1}{r e^{i θ}}$
$= \frac{e^{- i θ}}{r}$
$= \frac{r e^{- i θ}}{r^{2}}$
$= \frac{¯ z}{| z |^{2}}$ .
Hence the multiplicative inverse of $z$ is
$= \frac{¯ z}{| z |^{2}}$

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