It is known that the hybrid numbers are generalizations of complex, hyperbolic and dual numbers. Recently, they have attracted the attention of many scientists. At this paper, we provide the Euler’s and De Moivre’s formulas for the 4×4 matrices associated with hybrid numbers by using trigonometric identities. Also, we give the roots of the matrices of hybrid numbers. Moreover, we give some illustrative examples to support the main formulas.
I wanted to find an idea that was easier than L’Hospital’s rule and Trigonometric identities forsolving limits approaching zero because it is often very hard to solve these limits with existingideas. This is an idea that succeeds in making it easier to solve these limits. I wanted to show thisidea so that it could become a recognized part of Mathematics as we understand it. This can notonly be useful to anyone who has to deal with limits approaching zero (think electricians withAC current) but also useful to those who will prove new concepts in Calculus with this postulate.This idea should be used because it is easier to use than L’Hospital’s rule and Trigonometricidentities. It also lends itself to proving other arguments very well. It is also faster than existingmethods and mathematically sound. This is an explanation of a new concept.
Appendix F: Trigonometric Identities
