p-complex Fibonacci and Lucas numbers

This study consists of five parts. The studies which are related to the literatüre are given in the first part. In the second part of this study; complex, dual, hyperbolic and generalized complex numbers' definitions and their algebraic properties are given. In the third part; Fibonacci, Lucas and generalized Fibonacci numbers' sequences are defined and given the identities which includes them. In the fourth part which is the original section of this thesis, complex Fibonacci, Lucas numbers and complex generalized Fibonacci numbers which are complex, dual and hyperbolic numbers' general form is defined and investigated of these numbers' algebraic properties. In addition to these, the equalities such as Binet, Cassini, Catalan, d'Ocagne and Pythagorean are examined. In this process, the identities which include Fibonacci, Lucas and generalized Fibonacci numbers are used. Debates and results about complex Fibonacci, Lucas numbers and generalized Fibonacci numbers are given in the last section.