The inverse of $ z $ is:
$$ z^{-1} = 2 $$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
$$ z_1 = \frac{1}{ \frac{ 1 }{ 2 } } $$Step 2: Multiply top and bottom by complex conjugate of $ z $
$$ z_1 = \frac{1}{ \frac{ 1 }{ 2 } } \cdot \frac{ \frac{ 1 }{ 2 } }{ \frac{ 1 }{ 2 } } $$Step 3: Simplify
$$ z_1 = \frac{ \frac{ 1 }{ 2 } }{ \frac{ 1 }{ 4 } } $$$$ z_1 = \frac{ \frac{ 1 }{ 2 } }{ \frac{ 1 }{ 4 } } + \frac{ 0 }{ \frac{ 1 }{ 4 } } \cdot i$$$$ z_1 = 2 $$