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2. Show that the general linear transformation T(z) = az + b, where a and bare complex constants, is the composition of a rotation, followed by a dilation, followed by a translation. Hint

2. Show that the general linear transformation T(z) = az + b, where a and bare complex constants, is the composition of a rotation, followed by a dilation, followed by a translation. Hint

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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polic -tion Vi DULC .A? 2. Show that the general linear transformation T(z) = az + b. where a and bare complex constants, is the composition of a rotation, followed by a dilation, followed by a translation. Hint View the complex constant a in polar form. to 3. Prove that a general linear transformation maps circles to circles.
Transcribed Image Text:polic -tion Vi DULC .A? 2. Show that the general linear transformation T(z) = az + b. where a and bare complex constants, is the composition of a rotation, followed by a dilation, followed by a translation. Hint View the complex constant a in polar form. to 3. Prove that a general linear transformation maps circles to circles.
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