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
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