Section 2.6 The Reciprocal Transformation w = 1/z - Maple Application Center
Application Center Applications Section 2.6 The Reciprocal Transformation w = 1/z

Section 2.6 The Reciprocal Transformation w = 1/z

: Dr. John Mathews
Engineering software solutions from Maplesoft
This Application runs in Maple. Don't have Maple? No problem!
 Try Maple free for 15 days!
The mapping w = 1/z is called the reciprocal transformation and maps the z; plane one-to-one and onto the w; plane except for the point z = 0;, which has no image, and the point w = 0;, which has no preimage or inverse image. Using exponential notation w = rho*exp(i*phi);, we see that if z; = r*exp(i*theta) <> 0;, then we have w; = rho*exp(i*phi) = 1/z = 1/r; exp(i*theta);. It is convenient to extend the system of complex numbers by joining to it an "ideal" point denoted by infinity; and called the point at infinity. This new set is called the extended complex plane. The reciprocal transformation maps the "extended complex z-plane" one-to-one and onto the "extended complex w-plane"

Application Details

Publish Date: October 01, 2003
Created In: Maple V
Language: English



More Like This

Section 1.5 The Algebra of Complex Numbers, Revisited
Section 2.3 The Mappings w = z^n and w = z^`1/n`
Section 1.1 The Origin of Complex Numbers
Section 1.3 The Geometry of Complex Numbers
Section 2.1 Functions of a Complex Variable
Section 2.4 Limits and Continuity
Section 1.4 The Geometry of Complex Numbers, Continued
Section 2.2 Transformations and Linear Mappings
Section 1.2 The Algebra of Complex Numbers
Section 1.6 The Topology of Complex Numbers
Section 2.5 Branches of Functions
Section 3.1 Differentiable Functions