The inverse of $ z $ is:
$$ z^{-1} = 0.0256+0.0931i $$We will denote the inverse of $ z $ as $ z_1 $. The inverse can be found in three steps.
Step 1: Rewrite complex number as its reciprocal
$$ z_1 = \frac{1}{ 2.7472-9.9881i } $$Step 2: Multiply top and bottom by complex conjugate of $ z $
$$ z_1 = \frac{1}{ 2.7472-9.9881i } \cdot \frac{ 2.7472+9.9881i }{ 2.7472+9.9881i } $$Step 3: Simplify
$$ z_1 = \frac{ 2.7472+9.9881i }{ 107.3082 } $$$$ z_1 = \frac{ 2.7472 }{ 107.3082 } + \frac{ 9.9881 }{ 107.3082 } \cdot i$$$$ z_1 = 0.0256+0.0931i $$