Let z = cos + isin . Show that By considering (1 + z) n ,
Question:
Let z = cos θ + isin θ. Show that
By considering (1 + z)n, where n is a positive integer, deduce the sum of the series
Transcribed Image Text:
1+z = 2cos-0 cos -0 + isin-0
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 63% (11 reviews)
There are i dentities cos12cos1212cos cos0 and cos12sin1212sinsin0 Hence 2cos12cos12cos1 and 2icos...View the full answer
Answered By
Maria Virtanen
I'm completing my BSc in pure mathematics soon and will continue to MSc in applied mathematics. My strengths are in linear algebra, algebra, and linear programming, but I have great skills in one-variable calculus and geometry, too. In my spare time, I have given some advice in mathematics especially to students in engineering or business studies.
0.00
0 Reviews
10+ Question Solved
Related Book For
Cambridge International AS & A Level Further Mathematics Coursebook
ISBN: 9781108403375
1st Edition
Authors: Lee Mckelvey, Martin Crozier
Question Posted:
Students also viewed these Sciences questions
-
Let f(x) = c, where c is a positive constant. Explain why an area function of f is an increasing function.
-
Use recursion to compute an, where n is a positive integer. Hint: If n is 1, then a n = a. If n is even, then an = (a n/2 ) 2 . Otherwise, a n = a a n1 .
-
Approximate the sum of the series correct to four decimal places. a. b. (2n)! 1-n2 10
-
The following balance sheets were prepared for Pam Corporation and Slest Company on January 1, 20X2, just before they entered into a business combination: Pam acquired all of Slest Companys assets...
-
Suppose k, l, and m grow at constant rates given by k, l, and m. What is the growth rate of y in each of the following cases? (a) y = k1/3 (b) y = k1/3l2/3 (c) y = mk1/3l2/3 (d) y = mk1/4l3/4 (e) y =...
-
Four years ago Omega Technology, Inc., acquired a machine to use in its computer chip manufacturing operations at a cost of $35,000,000. The firm expected the machine to have a seven-year useful life...
-
(a) A rectangular loop of wire is \(\ell=800 \mathrm{~mm}\) long and \(w=500 \mathrm{~mm}\) wide. You bend the \(\ell\) sides into a semicircle while keeping the \(w\) sides straight, as shown in...
-
Flannery Company engages in the exploration and development of many types of natural resources. In the last two years, the company has engaged in the following activities: Jan. 1, 2016 ....Purchased...
-
8.The following data is available: Country Y currency Dollar Country X currency Peso Country Y interest rate 1% per year Country X interest rate 3% per year Country X expected inflation rate 2% per...
-
The Mach 10 is a one-person sailboat manufactured by Creative Leisure. The final assembly plant is in Cupertino, California. The assembly area is available for production of the Mach 10 for 200...
-
Simplify cos 5 + isin 5 , .giving your answer in an exponential form, where the terms are of the form ae ki .
-
On December 31,2018, Miller Company had $700,000 in total assets and owed $220,000 to creditors. If this corporation's common stock totaled $300,000, what amount of retained earnings is reported on...
-
Managerial accounting information is not just for accountants. All areas within an organization can use the information to support decision making. Choose a position in an organization that is...
-
All 4 parts to this question please. Thank you. It is all part of one question, use the information from the top. THANK YOU 1) Suppose Fuzzy Button Clothing Company's assets are fully utilized. Use...
-
Loss Carryforward The Bookbinder Company had $380,000 cumulative operating losses prior to the beginning of last year. It had $80,000 in pre-tax earnings last year before using the past operating...
-
Martinez Company's relevant range of production is 7,500 units to 12,500 units. When it produces and sells 10,000 units, its average costs per unit are as follows: Average Cost Per Unit Direct...
-
Marwick's Pianos, Incorporated, purchases pianos from a manufacturer for an average cost of $1,505 per unit and then sells them to retail customers for an average price of $2,600 each. The company's...
-
Problem Statement: Social Media Dashboard using Django Overview: You are tasked with creating a Social Media Dashboard using Django, allowing users to view and manage their social media activity from...
-
A bike is hanging from a hook in a garage. Consider the following forces: (a) The force of the Earth pulling down on the bike, (b) The force of the bike pulling up on the Earth, (c) The force of the...
-
The relationship described in question 7 does not always appear to hold. What factors, besides the number of firms in the market, might affect margins?
-
The smallest observed frequency for a transition between states of an electron in a one-dimensional box is 3.0 10 13 s 1 . What is the length of the box?
-
Are the total energy eigenfunctions for the free particle in one dimension, + (x) A + e +i(2mE/h2)x and (x) A e i(2mE/h2)x eigenfunctions of the one-dimensional linear momentum operator? If so,...
-
Use the eigenfunction (x) = Ae +ikx + Be ikx rather than (x) = A sin kx + B cos kx to apply the boundary conditions for the particle in the box. a. How do the boundary conditions restrict the...
-
0. Clarity of layout, logic, following color format, and instructions on page 1 and 2. [10 points] 1. You are a financial advisor. You have a client considering investing $22,000 in a high-growth...
-
Your medical office building is fully rented and has four tenants paying $1,150 per month. Operating expenses are $23,750 annually. You take out a first mortgage with a local bank with a monthly debt...
-
The Bluth Co., owner of the Balboa Towers Phase II, has secured a $50.0M, 10Y, 65% LTV mortgage that carries a 3.75% coupon. The debt is interest only for the first 5 years of the term. The in-place...
Study smarter with the SolutionInn App