The calculation of the long distance transmission line under constant alternating voltage

By separating real quantities and imaginaries in the general solution of the differential equations which express the relations which exist between the current and voltage at any point of a transmission line, the components of current, I
1
, and I
2
, and the components of voltage, V
1
and V
2
, are expressed as rational functions of the four quantities cosh αxcosβx, sinh αxsinβx, sinh αxcosβx, cosh αxsinβx.