TY - JOUR

T1 - Introducing complex numbers into basic growth functions - (VII) differences between '1' and '-1' in their hypothetic breakdown into complex numbers and application to definite integral of exp(t) expanded into infinite series

AU - Shimojo, Masataka

AU - Ikeda, Kentarou

AU - Asano, Yoki

AU - Ishiwaka, Reiko

AU - Sato, Hiroyuki

AU - Nakano, Yutaka

AU - Tobisa, Manabu

AU - Ohba, Noriko

AU - Eguchi, Minako

AU - Masuda, Yasuhisa

PY - 2005/10/1

Y1 - 2005/10/1

N2 - The present study was designed to investigate differences between '1' and '-1' in their hypothetic breakdown into complex numbers and application to definite integral of exp(t) expanded into infinite series. The results obtained were as follows. Complex numbers that were left by the hypothetic breakdown of product form in the complex representation of '1' and '-1' were classified into four groups according to properties of complex numbers; plus or minus, anti-clockwise or clockwise rotation on a circumference, hypothetic right-handed or left-handed spiral. Three groups or less showing an incomplete appearance of properties of complex numbers were derived from both '1' and '-1', but four groups that showed a complete appearance of all properties of them were derived from '1' only. This difference between '1' and '-1' might be due to the presence or absence of a minus sign. Complex numbers that were left by the hypothetic breakdown of product form in the complex representation of '1+(-1)' disappeared immediately in the calculation of growth using the definite integral of exp(t) expanded into infinite series.

AB - The present study was designed to investigate differences between '1' and '-1' in their hypothetic breakdown into complex numbers and application to definite integral of exp(t) expanded into infinite series. The results obtained were as follows. Complex numbers that were left by the hypothetic breakdown of product form in the complex representation of '1' and '-1' were classified into four groups according to properties of complex numbers; plus or minus, anti-clockwise or clockwise rotation on a circumference, hypothetic right-handed or left-handed spiral. Three groups or less showing an incomplete appearance of properties of complex numbers were derived from both '1' and '-1', but four groups that showed a complete appearance of all properties of them were derived from '1' only. This difference between '1' and '-1' might be due to the presence or absence of a minus sign. Complex numbers that were left by the hypothetic breakdown of product form in the complex representation of '1+(-1)' disappeared immediately in the calculation of growth using the definite integral of exp(t) expanded into infinite series.

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M3 - Article

AN - SCOPUS:27744465565

VL - 50

SP - 415

EP - 420

JO - Journal of the Faculty of Agriculture, Kyushu University

JF - Journal of the Faculty of Agriculture, Kyushu University

SN - 0023-6152

IS - 2

ER -