Complex Analysis Homework: Need Help Showing Statement is True

In summary, complex analysis is a branch of mathematics that focuses on the study of functions of complex numbers. This involves analyzing the behavior of functions in the complex plane and understanding their geometric properties. A statement in complex analysis is a mathematical proposition that can be either true or false and can be proven using rigorous techniques. To show a statement is true in complex analysis, one must use definitions, theorems, and properties of complex numbers and functions, as well as techniques like induction, proof by contradiction, or direct proof. Some common difficulties in proving statements in complex analysis include working in the complex plane and understanding the behavior of complex functions, which may be very different from real functions. If you need help with your complex analysis homework, you can seek
  • #1
asi123
258
0

Homework Statement



Hey guys.

I have this problem, I need to show that it's true and I don't have a clue.
I tried to do like alpha = x+yi but it got me nowhere, any ideas?

Thanks.


Homework Equations





The Attempt at a Solution

 

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  • #2
Try to show that

[tex]|1-\bar{\alpha}z|^2=|z-\alpha|^2[/tex] if and only if [tex]|z|^2=1[/tex]

and keep in mind that

[tex]|w|^2=w\bar{w}[/tex].
 
  • #3
yyat said:
Try to show that

[tex]|1-\bar{\alpha}z|^2=|z-\alpha|^2[/tex] if and only if [tex]|z|^2=1[/tex]

and keep in mind that

[tex]|w|^2=w\bar{w}[/tex].

Thanks.
 

FAQ: Complex Analysis Homework: Need Help Showing Statement is True

What is complex analysis?

Complex analysis is a branch of mathematics that deals with the study of functions of complex numbers. It involves analyzing the behavior of functions in the complex plane and understanding their geometric properties.

What is a statement in complex analysis?

A statement in complex analysis is a mathematical proposition that is either true or false. It is usually written in symbolic language and can be proven using rigorous mathematical techniques.

How do I show a statement is true in complex analysis?

To show that a statement is true in complex analysis, you will need to use the definitions, theorems, and properties of complex numbers and functions. You may also need to use techniques such as induction, proof by contradiction, or direct proof.

What are some common difficulties in proving statements in complex analysis?

Some common difficulties in proving statements in complex analysis include dealing with the complex plane, which is a two-dimensional space, and understanding the behavior of complex functions, which can be very different from real functions. Additionally, the use of complex numbers and their properties may be unfamiliar to some students.

How can I get help with my complex analysis homework?

If you need help with your complex analysis homework, you can seek assistance from your instructor or teaching assistant. You can also join study groups or seek help from online resources such as textbooks, videos, and forums. It is important to actively engage with the material and seek help early if you are struggling.

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