Introducing Complex Numbers into Basic Growth Functions- (,lV),Hypothetic Appearance of Exponential Function

This study was designed to. investigate the 'hypothetic appearance of ~xponential function wlth base e from the complex representation of 'O ~ (-1) + 1 ' and phase shifts. The results obtained were as follows. There was a hypothetic appearahce'of e~~(i6) froin the coinplex rep-re.sentation of '-1 ' in 'O = (-1) + 1 ' when subjected to the hyppthetic breakdown of multiplication form connecting complex numbers constructing '0 = (-1)+ 1'. The clockwise 7r/2 rotation of e ~rt exp(ie) Ied to exp(e). If there were many different complex numbers with their replicas to be I~ft, then this would b'e given by an equation with continuous phase shift of 6 in exp(i6). The hypothetic inheritance of phase shift of 6 in exp(i6) to the change in e in exp(6) might lead to the calculation of definite integral of exp(e). Might the change in 6 in exp(ie) and/or exp(6) be related to the passage of time (t) in exp(t)