A loss-less transmission line of length l is open-circuited and has characteristic impedance Z₀. The input impedance is 

Concept:

The input impedance in a transmission line is given by:

\({Z_{in}} = {Z_0}.\frac{{{Z_L} + j{Z_0}tanβ l}}{{{Z_0} + j{Z_L}tanβ l}}\)

'l' = Length of the line from the Load

β = 2π/λ = Wavenumber

Z0 = Characteristic Impedance of the Transmission Line

ZL = Load Impedance

Analysis:

For open-circuited load, Z_L ≈ ∞, the input impedance will be:

\({Z_{in}} = {Z_0}.\frac{{{Z_L}}}{{ j{Z_L}tanβ l}}\)

\({Z_{in}} = {Z_0}.\frac{{{1}}}{{ jtanβ l}}\)

Z_in = -Z₀ cot βl