Consider a function of z 1 j1, w e z (a) Find (i) log(w), (ii) Re(w), (iii) Im(w) (b) What is w w , where w is the complex conjugate of w (c) Determine w, w, and log(w) 2 (d) Express cos(1) in terms of w using Eulers identity ...

a If e z then log z 1 j1 given that the log and e functions are the inverse of each o ...

Consider a function of z = 1 + j1, w = e z (a) Find (i) log(w),

Question:

Consider a function of z = 1 + j1, w = e^z

(a) Find (i) log(w), (ii) Re(w), (iii) Im(w)

(b) What is w + w^*, where w^* is the complex conjugate of w?

(d) Express cos(1) in terms of w using Euler’s identity.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Signals and Systems using MATLAB

ISBN: 978-0123948120

2nd edition

Authors: Luis Chaparro

See More Books

Question Posted: Mar 13, 2020 09:30 AM

See More Questions

Re tan z and Im tan z. Show that
In each part, find Re (z) and Im (z). (a) z = 3ei (b) |= 2ei/2|
Consider the Euler equation for consumption for log utility, equation (16.8), and answer the following questions: (a) If the real interest rate is 5 percent and = 1, what growth rate for consumption...
Calculate the following ratios from the data given below: 1. Debt ratio 2. Debt service coverage multiples 3. Interest coverage Balance Sheet 12/31/2014 Assets Cash..$575,000 Short-term...
Researchers studied persons who had received intravenous immune globulin (IGIV) to see if they had developed infections of hepatitis C virus (HCV). In part of their analysis, they considered doses of...
Repeat Exercise 15.26 for water containing 0.324 mg/L of benzene (B) and 0.630 mg/L of m-xylene (X). Adsorption isotherms at 25C for these low concentrations are independent and given by The SOC...
3. Prove that a is a cluster point for some E ~ X if and only if there is a sequence Xn E E \ {a} such that Xn ---+ a as n ---+ 00.
Describe the importance of documentation under an SDLC methodology.
McBurger, Ino, wants to redesign its Achens to improve productivity and quality. Three designs, called designs K1, K2 and KS, are under consideration. No matter which design is used daily production...
Car dealers have realized how profitable it can be to sell automobiles by using the Web. Pretend that you work for a local car dealership that is part of a large chain such as CarMax. Create a system...
Consider the following problems related to computation with complex numbers. (a) Find and plot all roots of (i) z 3 = 1, (ii) z 2 = 1 (iii) z 2 + 3z + 1 = 0 (b) Suppose you want to find the natural...
A phasor can be thought of as a vector, representing a complex number, rotating around the polar plane at a certain frequency in radians/second. The projection of such a vector onto the real axis...
a. Develop a general Hasse diagram for a split- plot design with one whole- plot factor and two split-plot factors: Whole- plot factor A has a levels (i = 1, 2, c, a). Split- plot factor B has b...
E4.1 (LO 1), C The following independent situations require professional judgment for determining when to recognize revenue from the transactions. a. Southwest Airlines sells you an advance-purchase...
Spring Flings Company, a fashion retailer that specializes in colorful graphic tees, prepares a master budget on a quarterly basis. The company has assembled the following data to assist in preparing...
Find the linear approximation at the given point: f(x) = cos(4x-) at x =
The labor costs of complying with national regulations in order to remain a certified provider of testing products and services to oil producers. GeoTest creates, calibrates and installs devices used...
Mrs. Cora Yank (age 42) is divorced and has full custody of her 10-year-old son, William. Mrs. Yank works as a medical technician in a Chicago hospital. Her salary was $38,400, from which her...
Write a method maxOccurrences that accepts a list of integers as a parameter and returns the number of times the most frequently occurring integer (the mode) occurs in the list. Solve this problem...
Design a circuit which negative the content of any register and store it in the same register.
Suppose that you want to send an MP3 file to a friend, but your friends ISP limits the size of each incoming message to 1 MB and the MP3 file is 4 MB. Is there a way to handle this situation by using...
A large law firm, which has many employees, provides a single email address for each employee. Each employees email address is @lawfirm.com. However, the firm did not explicitly define the format of...
John wants to have an original domain name and uses a randomized program to generate a secondary domain name for him. He wants to register this domain name in the com generic domain. The domain name...
On finance.yahoo.com, type in "Shop" for "Shopify", and describe how its stock price has behaved over the last 3 years noting general patterns and any specific events or patterns that counter the...
IPO Costs. Match Group went public in November 2015. The company sold 33,333,333 shares at $12 per share. The underwriting spread was $0.66 a share, and the direct expenses were $0.21 a share. a....
true or false? question 35 An decrease in the discount rate rate will cause the present value of $100 that you will receive in the future to increase, True False

Consider a function of z = 1 + j1, w = e z (a) Find (i) log(w),

Question:

Step by Step Answer:

a If e z then log z 1 j1 given that the log and e functions are the inverse of each o...View the full answer

Signals and Systems using MATLAB

Students also viewed these Computer science questions