FIBONACCI AND THE COMPLEX PLANE
In 1963, A.F. Horadam of the University of New England, Armidale, Australia, examined Fibonacci numbers on the complex plane, and established some interesting properties about them . Two years later, J.H. Jordan of Washington State University followed up with a study of his own . We will now briefly study these numbers.
To begin with, we introduce the well-known Gaussian numbers. They were investigated in 1832 by the German mathematician Karl Friedrich Gauss (1777–1855), sometimes called the “prince of mathematics.”
30.1 GAUSSIAN NUMBERS
A Gaussian number is a complex number , where and are any integers, and . Its norm is defined by