1. The problem statement, all variables and given/known data Hey guys. I have a transmission line with a known characteristic impedance (50 Ω) of length L that is connected to an antenna that has a complex impedance of (50-j25)Ω. I am having extreme difficulty determining the minimum length (expressed in wavelengths) of line such that the input impedance is real. Let τ denote the reflection coefficient. I know that for the input impedance to have no complex component that (1+τ*e^(-jx))/(1-τ*e^(-jx)) should result in complex components vanishing. However, this is a rather complicated formula to solve in the state that it is in because both e^(-jx) and τ are complex numbers. Am I missing something here?