Consider an electrical circuit with a resistance ($R$), a coil ($L$) and a capacitor ($C$) in parallel. According to Kirchhoff's laws, the impedance $Z = Z(ω)$ of the circuit $RLC$ can be expressed, as a function of the angular frequency $ω$, by the equation $$ \frac{1}{Z} = \sqrt{\frac{1}{R^2}+\left(\omega C−\frac{1}{ωL}\right)^2\,}. $$
Considering $R = 225\Omega\, [\mathrm{ohm}]$, $C = 0.6 \times 10^{−6}F\, [\mathrm{farad}]$, $L = 0.5H\, [\mathrm{henry}]$, determine by Newton's method an approximate value of one of the values of $\omega$, which result in an impedance of $Z = 75\Omega$. Calculate $3$ iterations and obtain an error estimate for this approximation.