# Introducing complex numbers into basic growth functions - (IV) hypothetic appearance of exponential function with base e from the complex representation of '0=(-1)+1'

Masataka Shimojo, Kentaro Ikeda, Reiko Ishiwaka, Hiroyuki Sato, Yoki Asano, Manabu Tobisa, Yutaka Nakano, Noriko Ohba, Minako Eguchi, Yasuhisa Masuda

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

## Abstract

This study was designed to investigate the hypothetic appearance of exponential function with base e from the complex representation of '0=(-1)+1' and phase shifts. The results obtained were as follows. There was a hypothetic appearance of exp(iθ) from the complex representation of '-1' in '0=(-1)+1' when subjected to the hypothetic breakdown of multiplication form connecting complex numbers constructing '0=(-1)+1'. The clockwise π/2 rotation of θ in exp(iθ) led to exp(θ). If there were many different complex numbers with their replicas to be left, then this would be given by an equation with continuous phase shift of θ in exp(iθ). The hypothetic inheritance of phase shift of θ in exp(iθ) to the change in θ in exp(θ) might lead to the calculation of definite integral of exp(θ). Might the change in θ in exp(iθ) and/or exp(θ) be related to the passage of time (t) in exp(t)?

Original language English 349-353 5 Journal of the Faculty of Agriculture, Kyushu University 49 2 Published - Oct 2004

## All Science Journal Classification (ASJC) codes

• Agricultural and Biological Sciences (miscellaneous)

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