# Complex analysis and linear algebra

Exercise 7. The family of mappings introduced here plays an important role in complex analysis. These mappings, sometimes called Blaschke factors, will reappear in various applications in later chapters.

(1) Let z, w be two complex numbers such that zw 6= 1. Prove that w − z 1 − wz < 1 if |z| < 1 and |w| < 1, and also that w − z 1 − wz = 1 if |z| = 1 or |w| = 1.

(2) Prove that for a fixed w in the unit disc D, the mapping F : z 7→ w − z 1 − wz satisfies the following conditions

(a) F maps the unit disc to itself (that is, F : D → D), and is holomorphic.

(b) F interchanges 0 and w, namely F(0) = w and F(w) = 0.

(c) |F(z)| = 1 if |z| = 1.

(d) F : D → D is bijective.

Pages (550 words)
Approximate price: -

Why Choose Us

Quality Papers

We value our clients. For this reason, we ensure that each paper is written carefully as per the instructions provided by the client. Our editing team also checks all the papers to ensure that they have been completed as per the expectations.

Over the years, our Acme Homework has managed to secure the most qualified, reliable and experienced team of writers. The company has also ensured continued training and development of the team members to ensure that it keep up with the rising Academic Trends.

Affordable Prices

Our prices are fairly priced in such a way that ensures affordability. Additionally, you can get a free price quotation by clicking on the "Place Order" button.

On-Time delivery

We pay strict attention on deadlines. For this reason, we ensure that all papers are submitted earlier, even before the deadline indicated by the customer. For this reason, the client can go through the work and review everything.

100% Originality

At Essay USA, all papers are plagiarism-free as they are written from scratch. We have taken strict measures to ensure that there is no similarity on all papers and that citations are included as per the standards set.

Our support team is readily available to provide any guidance/help on our platform at any time of the day/night. Feel free to contact us via the Chat window or support email: support@acmehomework.com.

Try it now!

## Calculate the price of your order

We'll send you the first draft for approval by at
Total price:
\$0.00

How it works?

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Our Services

Essay USA has stood as the world’s leading custom essay writing services providers. Once you enter all the details in the order form under the place order button, the rest is up to us.

## Essay Writing Services

At Essay USA, we prioritize on all aspects that bring about a good grade such as impeccable grammar, proper structure, zero-plagiarism and conformance to guidelines. Our experienced team of writers will help you completed your essays and other assignments.