The impedance of the given AC circuit containing resistor and inductor parallel to each other is 55.71 ohms.
The given parameters;
The inductive reactance is calculated as follows;
[tex]\omega _l = 2\pi fl\\\\\omega _l = 2\times 3.142 \times 2,000\times 10\times 10^{-3} = 125.68 \ ohms[/tex]
The impedance is the total opposition to the flow of current in the AC circuit and it is calculated as follows;
[tex]Z _{total} = \frac{1}{\frac{1}{Z_l} + \frac{1}{Z_R} } \\\\Z _{total} = \frac{1}{\frac{1}{125.68} + \frac{1}{100} }\\\\Z _{total} = 55.71 \ ohms[/tex]
Thus, the impedance of the given circuit is 55.71 ohms.
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