The inverse of $ z $ is:
$$ z^{-1} = -0.3446-0i $$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
$$ z_1 = \frac{1}{ -\frac{ 1451 }{ 500 }+0i } $$Step 2: Multiply top and bottom by complex conjugate of $ z $
$$ z_1 = \frac{1}{ -\frac{ 1451 }{ 500 }+0i } \cdot \frac{ -\frac{ 1451 }{ 500 }-0i }{ -\frac{ 1451 }{ 500 }-0i } $$Step 3: Simplify
$$ z_1 = \frac{ -\frac{ 1451 }{ 500 }-0i }{ 8.4216 } $$$$ z_1 = \frac{ -\frac{ 1451 }{ 500 } }{ 8.4216 } - \frac{ 0 }{ 8.4216 } \cdot i$$$$ z_1 = -0.3446-0i $$