## The Linear Fractional Transformation Of A Complex Variable: w=(az/b)/(cs/d)

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##### Authors

Fong, Humphrey

##### Advisor

##### Editor

##### Date of Issue

1964-04-01

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##### Citation

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##### Title

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

##### Other Titles

##### Type

thesis

##### 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.

##### Sponsors

##### Degree Awarded

Bachelor's

##### Semester

Spring

##### Department

Mathematics, Engineering & Computer Science