oroduced function re is based on the CC here (1-i)z* +(7+i)z f(z) = variable that will be replaced with complex numbers. The image is actually a picture of the complex plane, with the origin in the very center of the golden ring. The golden ring consists of those complex numbers that lie a distance between 0.9 and 1.1 units from the origin. The rules for coloring other complex numbers in the plane are as follows: given an initial complex number te not on the gold ring, f(z) is calculated. If the complex number f(z) lies somewhere on the gold ring, the original number2 colored the deepest shade of green. If not, the iterate f(z) is calculated. where again z is a 2z +6 If this result lies in the gold ring, the original z is colored a bluish shade of g not, the process continues up to the 12th iterate f (z), using a different color e time. If f(z) lies in the gold ring, z is colored red, and if not the process halts and green. each is colored black. The idea of recursion can be used to generate any number of similar images, w ith the end result usually striking and often surprising even to the creator. Exercises In each of the following problems, use the information given to determine a. (f +g)(-1 -(-1). See Examples 1,2, and 3. b. (f – g)(-1),c. (fg)(-1), and d. 2. f(-1)= 0 and g(-1)= -1 1. f(-1)=-3 and g(-1)= 5 4. f(x)= Vx and g(x)= x – 1 3. f(x)= x² – 3 and g(x) = x 6. f(x)= x+5 and g (x) = 6x %3D 5. f(-1)=15 and g(-1)=-3 7. f(x)= x* +1 and g(x) = x" +2 8. f(x)=°,% and g (x)= 9. f = {(5,2),(0, – 1),(-1, 3),(-2, 4)} and g = {(-1, 3),(0, 5)} 10. f = {(3, 15).(2, – 1).(-1, 1)} and g(x)=-2 %3D 2.
oroduced function re is based on the CC here (1-i)z* +(7+i)z f(z) = variable that will be replaced with complex numbers. The image is actually a picture of the complex plane, with the origin in the very center of the golden ring. The golden ring consists of those complex numbers that lie a distance between 0.9 and 1.1 units from the origin. The rules for coloring other complex numbers in the plane are as follows: given an initial complex number te not on the gold ring, f(z) is calculated. If the complex number f(z) lies somewhere on the gold ring, the original number2 colored the deepest shade of green. If not, the iterate f(z) is calculated. where again z is a 2z +6 If this result lies in the gold ring, the original z is colored a bluish shade of g not, the process continues up to the 12th iterate f (z), using a different color e time. If f(z) lies in the gold ring, z is colored red, and if not the process halts and green. each is colored black. The idea of recursion can be used to generate any number of similar images, w ith the end result usually striking and often surprising even to the creator. Exercises In each of the following problems, use the information given to determine a. (f +g)(-1 -(-1). See Examples 1,2, and 3. b. (f – g)(-1),c. (fg)(-1), and d. 2. f(-1)= 0 and g(-1)= -1 1. f(-1)=-3 and g(-1)= 5 4. f(x)= Vx and g(x)= x – 1 3. f(x)= x² – 3 and g(x) = x 6. f(x)= x+5 and g (x) = 6x %3D 5. f(-1)=15 and g(-1)=-3 7. f(x)= x* +1 and g(x) = x" +2 8. f(x)=°,% and g (x)= 9. f = {(5,2),(0, – 1),(-1, 3),(-2, 4)} and g = {(-1, 3),(0, 5)} 10. f = {(3, 15).(2, – 1).(-1, 1)} and g(x)=-2 %3D 2.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.2: Complex Numbers And Quaternions
Problem 36E
Related questions
Question
Transcribed Image Text:oroduced
function
re
is
based
on
the
CC
here
(1-i)z* +(7+i)z
f(z) =
variable that will be replaced with complex
numbers. The image is actually a picture of
the complex plane, with the origin in the
very center of the golden ring. The golden
ring consists of those complex numbers
that lie a distance between 0.9 and 1.1 units
from the origin. The rules for coloring
other complex numbers in the plane are as
follows: given an initial complex number te
not on the gold ring, f(z) is calculated. If
the complex number f(z) lies somewhere on the gold ring, the original number2
colored the deepest shade of green. If not, the iterate f(z) is calculated.
where again z is a
2z +6
If this result lies in the gold ring, the original z is colored a bluish shade of g
not, the process continues up to the 12th iterate f (z), using a different color e
time. If f(z) lies in the gold ring, z is colored red, and if not the process halts and
green.
each
is colored black.
The idea of recursion can be used to generate any number of similar images, w ith the
end result usually striking and often surprising even to the creator.
Exercises
In each of the following problems, use the information given to determine a. (f +g)(-1
-(-1). See Examples 1,2, and 3.
b. (f – g)(-1),c. (fg)(-1), and d.
2. f(-1)= 0 and g(-1)= -1
1. f(-1)=-3 and g(-1)= 5
4. f(x)= Vx and g(x)= x – 1
3. f(x)= x² – 3 and g(x) = x
6. f(x)=
x+5
and g (x) = 6x
%3D
5. f(-1)=15 and g(-1)=-3
7. f(x)= x* +1 and g(x) = x" +2
8. f(x)=°,% and g (x)=
9. f = {(5,2),(0, – 1),(-1, 3),(-2, 4)} and g =
{(-1, 3),(0, 5)}
10. f = {(3, 15).(2, – 1).(-1, 1)} and g(x)=-2
%3D
2.
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