The inverse of $ z $ is:
$$ z^{-1} = -0.1345+0.1037i $$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
$$ z_1 = \frac{1}{ -4.6613-3.5949i } $$Step 2: Multiply top and bottom by complex conjugate of $ z $
$$ z_1 = \frac{1}{ -4.6613-3.5949i } \cdot \frac{ -4.6613+3.5949i }{ -4.6613+3.5949i } $$Step 3: Simplify
$$ z_1 = \frac{ -4.6613+3.5949i }{ 34.6504 } $$$$ z_1 = \frac{ -4.6613 }{ 34.6504 } + \frac{ 3.5949 }{ 34.6504 } \cdot i$$$$ z_1 = -0.1345+0.1037i $$