Franco-Rodriguez, Jorge Adalberto
Mathematics and Applied Mathematics
October 4, 2019
Vectors, Complex Numbers, Complex Vectors, Dot And Cross Product
A normal vector r is that whose components (x, y, z) are scalars. This work shows that the components in a complex vector are instead complex numbers, of the form (ai+jbi), for j=√(-1). So, each component has a real and an imaginary part and conceptually both are conceived perpendicular to each other. This work finds the way to take into account these aspects and introduces a new approach to construct and define N-dimensional complex vectors and how to obtain correctly their properties and characteristics. Obtained multidimensional complex vectors allowed calculating the N-dimensional Dot and Cross product. Complex Vector’s properties and their differences with scalars, complex numbers and pure vectors are discussed.