= Solution
Write $X=1/(\omega C)=200\,\Omega$. The magnitude of the <series RC impedance> is
$$
\boxed{Z_m=\sqrt{R^2+X^2}=\sqrt{100^2+200^2}=223.61\,\Omega.}
$$
For independent small errors interpreted as <standard uncertainties>, <propagation of uncertainty> gives
$$
u(Z_m)^2=\left(\frac R{Z_m}u_R\right)^2+\left(\frac{X^2}{Z_m}\frac{u_\omega}{\omega}\right)^2+\left(\frac{X^2}{Z_m}\frac{u_C}{C}\right)^2.
$$
The input uncertainties are $u_R=2\,\Omega$, $u_\omega/\omega=0.01$, and $u_C/C=0.01$. Thus $u(Z_m)^2=0.80+3.20+3.20=7.20\,\Omega^2$, and
$$
\boxed{|Z|=(223.6\pm2.7)\,\Omega\quad\text{with independent standard uncertainties}.}
$$
The fractional uncertainty is $1.20\%$. If the stated errors are instead worst-case bounds, their first-order contributions add in magnitude, giving approximately $4.47\,\Omega$, or $2.0\%$, rather than the quadrature result. Both conventions require the error interpretation to be specified.
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