The Polar form of a Neutrosophic Complex Number

Department Of Mathematics, College Of Science, Alfurat University, Deir-Ez-Zor, Syria , ,Admin Admin,Mayas Ismail,Florentin Smarandache

doi:10.54216/ijns.0100103

Department Of Mathematics, College Of Science, Alfurat University, Deir-Ez-Zor, Syria , + Show 3 more

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https://doi.org/10.54216/ijns.0100103

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Abstract

In this paper, we will define the exponential form of a neutrosophic complex number. We have proven some characteristics and theories, including the conjugate of the exponential form of a neutrosophic complex number, division of the exponential form of a neutrosophic complex numbers, multiplication of the exponential form of a neutrosophic complex numbers. In addition, we have given the method of changing from the exponential to the algebraic form of a complex number.

Highlights

Smarandache presented the definition of the standard form of neutrosophic real number and conditions for the division of two neutrosophic real numbers to exist, he defined the standard form of neutrosophic complex number [24], and Y
Alhasan presented the properties of the concept of neutrosophic complex numbers including the conjugate of neutrosophic complex number, division of neutrosophic complex numbers, the inverted neutrosophic complex number and the absolute value of a neutrosophic complex number and theories related to the conjugate of neutrosophic complex numbers, and that the product of a neutrosophic complex number by its conjugate equals the absolute value of number [25]
3. The Polar form of a Neutrosophic Complex Number we present and study the exponential form of a neutrosophic complex number

Summary

Introduction

Definition 2.1 [24] A neutrosophic number has the standard form: a+b where a, b are real or complex coefficients, and I = indeterminacy, such 0.I = 0 = for all positive integer n. Definition 2.2 [25] z is a neutrosophic complex number, if it takes the following standard form:. Definition 3.1 We define the Exponential Form of a Neutrosophic Complex Number as follows:. The formula neutrosophically works in the following way: x = a+bI is a neutrosophic number whose determinate part is "a" and indeterminate part is "bI", where I = indeterminacy; y = c+dI is a neutrosophic number whose determinate part is "c" and indeterminate part is "dI"; Θ = θ + I is a neutroosphic angle, whose determinate part is Θ ("theta") and indeterminate part is "I". Properties we present some important properties of the exponential form

Multiplying the exponential forms of the neutrosophic complex numbers

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