The inverse of $ z $ is:
$$ z^{-1} = \frac{ 19 }{ 7995 }+\frac{ 16 }{ 2665 }i $$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
$$ z_1 = \frac{1}{ 57-144i } $$Step 2: Multiply top and bottom by complex conjugate of $ z $
$$ z_1 = \frac{1}{ 57-144i } \cdot \frac{ 57+144i }{ 57+144i } $$Step 3: Simplify
$$ z_1 = \frac{ 57+144i }{ 23985 } $$$$ z_1 = \frac{ 57 }{ 23985 } + \frac{ 144 }{ 23985 } \cdot i$$$$ z_1 = \frac{ 19 }{ 7995 }+\frac{ 16 }{ 2665 }i $$