What impedance does a 1/8-wavelength transmission line present to an RF generator when the line is shorted at the far end?
Why For a shorted line the input impedance is jZ0 tan(theta), where theta is the electrical length. At 1/8 wavelength theta is 45 degrees, so the input impedance is +jZ0, a purely inductive reactance whose magnitude equals the characteristic impedance. Any shorted line shorter than 1/4 wavelength looks inductive; it only becomes a parallel-resonant open circuit at exactly 1/4 wavelength.
Watch out Capacitive reactance is what a 1/8-wavelength line with an open far end presents, since an open line behaves the opposite way from a shorted one. The choice saying zero would only apply to a short line very much shorter than 1/8 wavelength, or a half-wavelength line, which repeats the short.
Short stays short: shorted stub under 1/4 wave acts inductive; open stub under 1/4 wave acts capacitive.