dc.contributor.author | Fong, Humphrey | |

dc.date.accessioned | 2020-04-30T10:08:53Z | |

dc.date.available | 2020-04-30T10:08:53Z | |

dc.date.issued | 1964-04-01 | |

dc.identifier.uri | https://scholars.carroll.edu/handle/20.500.12647/3504 | |

dc.description.abstract | A complex number is represented in rectangular coordinates as x/iy, where x and y are real. It is also represented as r(cos e/i sin e) in polar coordinates, where r and e are real. r is called the absolute value, or modulus of the complex number, and e its amplitude. Graphically, a complex number can be represented as a pt. (x,y) or (r,e) in the complex plane. It can also be thought of as a vector from the origin to the pt. (r,e), with length r and angle of inclination e.
The complex numbers form a field, and hence possess all the properties of a field. Only two of the properties of the complex numbers will be stated here:
(1) IF z=r(cos e/i sin e) , z'=r'(cos e'/i sin e')
then, zz'=rr'[cos(e/e')/i sin(e/e')]
(2) Let z be the complex conjugate of z. Geometrically, z is obtained by reflecting z upon the x-axis. | |

dc.title | The Linear Fractional Transformation Of A Complex Variable: w=(az/b)/(cs/d) | |

dc.type | thesis | |

carrollscholars.object.degree | Bachelor's | |

carrollscholars.object.department | Mathematics, Engineering & Computer Science | |

carrollscholars.object.disciplines | Mathematics | |

carrollscholars.legacy.itemurl | https://scholars.carroll.edu/mathengcompsci_theses/128 | |

carrollscholars.legacy.contextkey | 13043433 | |

carrollscholars.object.season | Spring | |

dc.date.embargo | 12/31/1899 0:00 | |