WORKING METHODS OF CALCULATION 81 



In using complex quantities with alternating-current 

 problems, quantities which are in quadrature, that is, 

 which have 90 lead or lag, are called imaginary and 

 are multiplied by j. Thus, a quadrature current and 

 a reactance are both multiplied byj', and when they are 

 multiplied together in order to obtain the voltage drop, 

 the drop is found to be a negative quantity, that is, 

 it has 1 80 lag, which agrees with the physical fact 

 that a quadrature current through a reactance has a 

 negative in-phase voltage drop. It is found that the 

 mathematical properties of complex quantities agree 

 completely with the physical characteristics of alternating 

 currents of sine wave form, and that complex quantities 

 furnish the easiest means of calculating the results in- 

 dicated by vector diagrams. 



For calculating the convergent series for transmis- 

 sion lines, Y and Z are first written down as complex 

 numbers. The necessary data can be obtained from 

 tables of resistance, reactance, and capacity susceptance. 

 The leakage conductance is generally omitted from en- 

 gineering calculations, as it is due to insulator leakage 

 and corona loss, which ought not, for good practice, to 

 be appreciable at the operating voltage. By multiplying 

 the complex quantities Y and Z, the product Y Z may 

 be obtained as a complex number composed of a single 

 real term and a single j term. From this are obtained 



YZ YZ YZ 



, and 7-, 



2 ' 4 6 ' 



and by multiplying again, 



F 2 Z 2 F 2 Z 2 



and 



2.3.4 2.3.4.5 



