# 数学复数作业代写 MAT334 Complex Variables

## MAT334 Complex Variables

### Instructions  数学复数作业代写

This homework is based on week 3. Please read the Homework Policies for details on submission policies, collaboration rules, and general instructions.

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### Date:Signature:  数学复数作业代写

1. In this question, you will disect a bad argument using branches. Consider the claim below:

The argument below is incomplete and possibly incorrect.  数学复数作业代写

(1a) (1 point) Line 2 is trying to show something about the number g(f (z)) for some fixed z. Precisely state what it is trying to show. (Note: it is not showing anything about the function g(f (z)).)
(1b) (1 point) Line 3 claims that line 2 shows g(f (z)) is a branch. However, it is not fully justified. What else do you need to show to conclude it is a branch?
(1c) (1 point) Finish properly justifying line 3.
(1d) (1 point) Line 4 does not consider every situation where g(f (z)) is not defined. What other case needs to be handled?
(1e) (1 point) Find the actual domain of g(f (z)) by finishing the argument.

### 2. Let arg0  数学复数作业代写

(z) be the branch of the argument with arg0 (z) ∈ In this question, you will prove that g(z) = f (f (z)) is a branch o

(2a) (4 points) The claim that g(z) is a branch ois really two smaller claims. Precisely state these smaller claims and explain why these claims show g is a branch o

(2b) (1 point) Prove that g is a brach o