Show that cos z is one-to-one.
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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[Complex Analysis] How do you solve this? The question is the bullet point
Note that the two deleted rays in the picture are incorrect and are supposed to be (-inf, -1] and [1, inf), respectively
Transcribed Image Text:Show that cos z is one-to-one.
![4.
Consider the function w = cos z and the following two sets
D = {z = x+ yi E C, 0 < x < n}
R= C/{w €R, ]w] > 1}
i.e., R is the complex plane deleting two rays (-0, –1] and [1, –x) on
the real axis. Now take D as the domain of definition for f(z) = cos z
w=cos(z)
Figure 1: graph of w = cos z : D → R](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94cfc6b7-9d0a-4d76-a32e-6be09f8470c1%2Fd5026cb8-2f55-478f-84c4-236b6d742c89%2Fwplptba_processed.png&w=3840&q=75)
Transcribed Image Text:4.
Consider the function w = cos z and the following two sets
D = {z = x+ yi E C, 0 < x < n}
R= C/{w €R, ]w] > 1}
i.e., R is the complex plane deleting two rays (-0, –1] and [1, –x) on
the real axis. Now take D as the domain of definition for f(z) = cos z
w=cos(z)
Figure 1: graph of w = cos z : D → R
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