equation of a line through two complex numbers

i dont understand how this equation can be: http://www.transtutors.com/userfiles/image/ARUN/Fold/eq4.JPG
because if i have two complex numbers and put them in this equation i will get out 0, in a normal equation of a line ax+b = c i have one variabel x, i dont see how we can have a equation of a line without this variabel in complex numbers. maybe i would be less confused if you had an example. lets say A= i and Z= 1+2i. what would be the equation through this line?