I am seeing in "slow motion" the development of vectorial system. I am reading the book "A History of Vector Analysis" (by Michael J.Crowe); it seems from my acquaintance that the vector concept came from the quaternions concept; and the quaternions concept came from the act of search for geometrical representation of complex numbers. And these complex numbers drops down to the concept of √(negative numbers); if complex numbers were true numbers, there is no need for the search of another geometrical representation, as we already have cartesian coordinate system. But, of course, they don't seem to be any usual negative or positive numbers. I thought these numbers to be non-sense (one which doesn't make sense). It seems Gauss, Argand, Buee, Mourey. Warren and Hamilton (?) tried to find a geometrical representation for complex numbers. According to the angle in which my analysis is going, I don't understand what motivated these all to find a geometrical representation (gr) for Complex numbers. In no thinking route of mine suggest me to find a gr. So, the question is what motivated all these folks to search for a gr of complex numbers? Is gr (of complex numbers) an invention or discovery? I will be happy if important books and papers are suggested in this regard.