The nominal-π line model has series impedance $Z=100\angle80^\circ\ \Omega$ and each shunt branch has capacitive reactance magnitude X=3300 Ω. Find the line characteristic-impedance magnitude in ohms, to one decimal place.
In the nominal lumped approximation, use total shunt admittance $Y=2j/X$, since both end branches contribute. The characteristic-impedance estimate is $Z_c\approx\sqrt{Z/Y}$.
Its magnitude is $\sqrt{|Z|/|Y|}=\sqrt{100(3300)/2}=406.2019$ Ω. Rounded to one decimal place, this is **406.2 Ω**, within the official 404–409 Ω interval.
This is the distributed-line characteristic estimate from the nominal series/shunt quantities, not the exact image impedance of a finite π two-port.
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