THE GRADIENT AND PARTIAL DERIVATIVES OF BICOMPLEX NUMBERS: A COMMUTATIVE-QUATERNION APPROACH

Abstract

The study of bicomplex numbers, specifically commutative-quaternions, offers a fascinating exploration into the properties of complexified quaternions with commutative multiplication. Understanding the gradient and partial derivatives within this mathematical framework is crucial for analyzing the behavior of bicomplex functions. Real quaternions are not commutative but bicomplex numbers are commutative by multiplication. Bicomplex numbers are the special case of real quaternions. In this study, gradient and partial derivatives are obtained for bicomplex number valued functions.

Keywords

• Bicomplex number
• Quaternion
• Partial derivate
• Gradient

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