Introducing complex numbers into basic growth functions - (III) symmetry breakdown in complex representation of '0=(-1)+1' in definite integral of exponential function with base e expanded into infinite series

The present study was designed to investigate various types of symmetry breakdown that left complex numbers by giving a minus sign to each of the odd-numbered pieces of complex number out of eight constructing T. The results obtained were as follows. Giving a minus sign to each of the odd-numbered (1, 3, 5, 7) pieces of complex number out of eight changed '1' into '-1'. The hypothetic breakdown of multiplication form that connected complex numbers to construct '-1' left one or three sorts of complex numbers. The symmetry breakdown, which was given by the breakdown of multiplication form, was larger when a minus sign was given to each of the three and five pieces of complex number than when given to one piece and each of the seven pieces out of eight. The larger symmetry breakdown left more pieces of complex number.