To investigate number of zeros of a quaternion polynomial inside a given region over the skew field

Abstract

This work deal with the behaviour of quaternion function, like continuity, differentiability and the necessary condition for differentiability. We are discussing some important behaviour of quaternion polynomials and trying to convert Rouche's Theorem of complex version into quaternion form. For this, we are trying to convert Argument Theorem of complex form into quaternion form. To prove Argument Theorem we are trying to prove Cauchy-Gaursat Theorem into quaternion form. We are trying to find NecessaryCondition for differentiability into quaternion form of a given quaternion function. We are trying to establish the quaternion version of Green's theorem.