De-Moivre formula for dual-complex numbers

This thesis consists of four chapters. The first chapter is the introduction. In the second part, Real, Complex and Dual quaternions are introduced. De-Moivre and Euler formulae are given for Real, Complex and Dual quaternions. The third part is the original part of the thesis. The original part of the thesis is organized in five sub-sections. In the fırst chapter, algebraic strutures of dual-complex numbers are introduced and trigonometric values are given. Then the exponential representation of the dual-complex numbers is derived and the Euler formula is given. Finally, logarithmic and matrix representations of dual-complex numbers are given. In the fourth chapter of this thesis, the general evaluation of the study is given and a suggestion is proposed for further investigations.