Skip to main content
guest
Join

Help

Sign In
complexworld
Home
guest

Join

Help

Sign In
Wiki Home
Recent Changes
Pages and Files
Members
Favorites
20
All Pages
20
home
1.4.12
2.2 q1418
Final exam
Homework 1
Homework 2
Images and preimages
Incomplete lecture 9 notes
List of most confusing topics
Midterm
Midterm Summer 2011
Mobius transformations
Previous exams
Questions
Quiz 1
Quiz 1 Summer 2011
Quiz 2
Quiz 2 Summer 2011
Quiz 3
Quiz 3 Summer 2011
see more
Add
Add "All Pages"
Done
Quiz 1 Summer 2011
Edit
0
6
…
0
Tags
No tags
edit
Save
Cancel
Notify
RSS
Backlinks
Source
Print
Export (PDF)
1.
Find all complex numbers z satisfying
Do not use trigonometric or exponential functions in your answer.
Solution:
hence
2.
Is the set
open, closed or neither open nor closed? Is it connected? Sketch its boundary and state whether it is open, closed or neither open nor closed.
Solution:
The set is neither open nor closed. It is not connected. The boundary is the union of the circle
with the horizontal rays
and
The boundary is closed.
3.
Sketch the preimage of the set
under the map f(z)=z^2+1+i. Is it connected?
Solution:
The preimage is the union of the two sets
and
Javascript Required
You need to enable Javascript in your browser to edit pages.
help on how to format text
Turn off "Getting Started"
Home
...
Loading...
Find all complex numbers z satisfying
Do not use trigonometric or exponential functions in your answer.
Solution:
hence
2.
Is the set
open, closed or neither open nor closed? Is it connected? Sketch its boundary and state whether it is open, closed or neither open nor closed.
Solution:
The set is neither open nor closed. It is not connected. The boundary is the union of the circle
with the horizontal rays
and
The boundary is closed.
3.
Sketch the preimage of the set
under the map f(z)=z^2+1+i. Is it connected?
Solution:
The preimage is the union of the two sets
and