Find the multiplicative inverse of $- i$

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Solution

Given data: $z = - i$
Using the concept of multiplicative inverse.
$z^{- 1} = \frac{1}{- i}$
Now, using rationalization method

$z^{- 1} = \frac{1}{- i} \times \frac{i}{i} = \frac{i}{- (i)^{2}} = \frac{i}{1}$
$z^{- 1} = i$

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