The inverse of $ z $ is:
$$ z^{-1} = \frac{ 1235 }{ 12204112 }+\frac{ 17 }{ 12204112 }i $$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
$$ z_1 = \frac{1}{ 9880-136i } $$Step 2: Multiply top and bottom by complex conjugate of $ z $
$$ z_1 = \frac{1}{ 9880-136i } \cdot \frac{ 9880+136i }{ 9880+136i } $$Step 3: Simplify
$$ z_1 = \frac{ 9880+136i }{ 97632896 } $$$$ z_1 = \frac{ 9880 }{ 97632896 } + \frac{ 136 }{ 97632896 } \cdot i$$$$ z_1 = \frac{ 1235 }{ 12204112 }+\frac{ 17 }{ 12204112 }i $$