Question

In: Advanced Math

We are working on functions of complex variables in calculus (Chpt. 17.4 in Advanced Engineering Mathematics),...

We are working on functions of complex variables in calculus (Chpt. 17.4 in Advanced Engineering Mathematics), and our prof posed us the following question:

"Find the function w = u + iv = f(z) that maps the region S := {z : 0 ≤ arg z ≤ π 4 } to the upper half plane {w = u + iv : v ≥ 0}."

the answer he gave to this problem was as follows: "such a mapping is given by f(z) = z^4 = r^4*e^4iθ where z = re^iθ ."

I am unsure how he came to this conclusion, could someone please help? Thanks!

Solutions

Expert Solution

Colby Messinger answered 2 years ago
Next > < Previous

Related Solutions

1 Program Summary We are subcontractors for the Corellian Engineering Corportation (CEC) and we are working...
1 Program Summary We are subcontractors for the Corellian Engineering Corportation (CEC) and we are working on one of the subsystems for the MC85 star cruiser. Our task is to model stress on a particular surface of the cruiser. Stress is defined as σ = Ld Area , where Ld is the load and Area is the area. Let’s say we are working with the metric measure system. So the load would be in kilograms. Area would be meters. We...
1 Program Summary We are subcontractors for the Corellian Engineering Corportation (CEC) and we are working...
1 Program Summary We are subcontractors for the Corellian Engineering Corportation (CEC) and we are working on one of the subsystems for the MC85 star cruiser. Our task is to model stress on a particular surface of the cruiser. Stress is defined as σ = Ld Area , where Ld is the load and Area is the area. Let’s say we are working with the metric measure system. So the load would be in kilo grams. Area would be meters....
In SQL we are working with functions 1. Write a SELECT statement that returns these columns...
In SQL we are working with functions 1. Write a SELECT statement that returns these columns from the Instructors table: a. The AnnualSalary column b. A column named MonthlySalary that is the result of dividing the AnnualSalary column by 12 c. A column named MonthlySalaryRounded that calculates the monthly salary and then uses the ROUND function to round the result to 2 decimal places 2. Write a SELECT statement that returns these columns from the Students table: a. The EnrollmentDate...
We will use shorthand notation and probability notation for random variables when working with normally distributed...
We will use shorthand notation and probability notation for random variables when working with normally distributed random variables. Suppose the vitamin C content of a particular variety of orange is distributed normally with mean 720 IU and standard deviation 46 IU. If we designate X = the vitamin C content of a randomly selected orange, then our shorthand notation is X~N(720 IU, 46 IU). Use this distribution of vitamin C content to answer the following questions: 1) What is the...
We made the shift from working with discrete random variables back in Unit 2 to now...
We made the shift from working with discrete random variables back in Unit 2 to now working with continuous random variables. Highly important for the rest of the course is our ability to use the Normal Distribution, in which we either find a probability from a range of values of the normally distributed variable X or we find a range of values from a given probability. We will use shorthand notation (review LM 09 for how to use this notation)...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT