The inverse of $ z $ is:
$$ z^{-1} = 0.0002+0.348i $$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
$$ z_1 = \frac{1}{ 0.0014-2.8737i } $$Step 2: Multiply top and bottom by complex conjugate of $ z $
$$ z_1 = \frac{1}{ 0.0014-2.8737i } \cdot \frac{ 0.0014+2.8737i }{ 0.0014+2.8737i } $$Step 3: Simplify
$$ z_1 = \frac{ 0.0014+2.8737i }{ 8.2581 } $$$$ z_1 = \frac{ 0.0014 }{ 8.2581 } + \frac{ 2.8737 }{ 8.2581 } \cdot i$$$$ z_1 = 0.0002+0.348i $$