It may be noted in passing, however, that complex numbers have a close connection to vectors in 2 dimensions. Now, presumably, all the points on the line are covered. Mathematicians have invented all sort of strange generalizations of numbers. The ones of most interest are the ones with good applications . Vectors allow us to represent velocities .
Vectors help answer that.
Similarly, forces, accelerations, magnetc fields from several sources, all are added like vectors. Engineers who put up a bridge or a building and want to make sure all forces balance, etc., need vectors. You take a pencil and displace it from New York to Chicago , then from Chicago to Seattle . The final effect is the same as if we displaced the pencil from New York to Seattle . The displacement from New York to Chicago is this arrow.