A sinusoidal voltage source drives the series combination of an impedance, Z_g = 50 −  j50Ω, and a lossless transmission line of length L, shorted at the load end. The line characteristic impedance is 50Ω, and wavelength λ is measured on the line.

(a) Determine, in terms of wavelength, the shortest line length that will result in the voltage source driving a total impedance of 50 Ω.

(b) Will other line lengths meet the requirements of part (a)? If so, what are they?