We use complex arithmetic and algebra, as is normal in ac theory, to express both amplitude and phase angle information with a single symbol. A complex number is really just an ordered pair of numbers, having certain algebraic properties. All these quantities may be found with a calculator.
Most scientific calculators have a key for converting easily between polar and rectangular forms.
As the reflection coefficient gamma is also a dimensionless number this has the added advantage of simplifying the mathematics and making the understanding easier. Transmission lines having differing values of Zo all behave the same, as far as their normalised impedance properties are concerned. P along the line, where the actual impedance zZo is the local ratio of total voltage to total current taking into account the phase angles as well as the sizes. The voltages however, being measured from centre conductor to braid in each wave, are in the same sense in forward and backward waves. On a lossless line the current in the forward wave is in phase with the voltage, whereas the current in the backward wave is oppositely directed according to our sign convention.