Question: (a) Find the cube roots of 1. (b) Explain why the n nth roots of 1 when plotted in the complex plane lie on a

(a) Find the cube roots of 1.
(b) Explain why the n nth roots of 1 when plotted in the complex plane lie on a circle of radius 1 and are separated by an angle 2π/n from one another

Step by Step Solution

★★★★★

3.41 Rating (182 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Using Eq 136 with n 3 we have e i 0 1 e i 23 co... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

959-P-M-A-M (371).docx

120 KBs Word File

Students Have Also Explored These Related Mechanics Questions!

A cube has sides of length L = 0.300 m. It is placed with one comer at the origin as shown in Fig. The electric field is not uniform but is given by E = (-5.00 N/C .m) xi + (3.00 N/C .m) zk. (a) Find...

A skateboarder with his board can be modeled as a particle of mass 76.0 kg, located at his center of mass. As shown in Figure P8.67 on page 248, the skateboarder starts from rest in a crouching...

In example 3.4.1 we solved for x(n), n

806 Chapter Fifteen OPTIMIZATION: LOCAL AND GLOBAL EXTREMA If f is not continuous or the region R is not closed and bounded, there is no guarantee that f achieves a global maximum or global minimum...

We studied in basic algebra under complex numbers that the nth roots of unity. 2kx 2 = 1 z = (cos ( 24 ) :( cos( 2k ) + i sin (2Kr)). / k = 0,1...n-1 n selects in equally spaced points on the unit...

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

7-67 (Every fourth, and also 29, 33, 61, 65; pp.329-330 ) SECTION 3.5 . Complex Zeros and the Fundamental Theorem of Algebra 329 EXAMPLE 7 . Factoring a Polynomial into Linear and Quadratic Factors...

SOLVE Questions 1-5: PLEASE AND THANK YOU 1: What is the difference between homogenous and non-homogenous differential equation? Write an example for each and solve it. 2: What is the main formula to...

Finish every page 1.1: Problem Set Overview In this assignment you will be completing problems based on the parent functions we have learned in this topic. The purpose of this assignment is to...

lup ] (d) Show how a generating (or "mother") wavelet (x) can spawn a family of "daughter" wavelets jk(x) by simple shifting and scaling operations, and explain the advantages of representing...

A company manufactures and sells two products, S1 and S2. The total annual sales is expected to be R630 000 with a sales mix of 2:3 respectively. The contribution margin ratio of Product $1 is 40%,...

Consider a simple ideal Brayton cycle operating between the temperature limits of 300 and 1500 K. Using constant specific heats at room temperature, determine the pressure ratio for which the...

find the polynomial function with the given zeros 4 , - 3 , 3 , 0

Ken Jones, the number-one-ranked prizefighter in his weight class, signed a two-year contract with Howard Stayword. The contract obligated Stayword to represent and promote Jones in all business and...

Figure gives the torque r that acts on an initially stationary disk that can rotate about its center like a merry-go-round. The scale on the r axis is set by r?2 = 4.0 N ? m. What is the angular...

Figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed...

A disk with a rotational inertia of 7.00 kg m2 rotates like a merry-go-round while undergoing a torque given by = (5.00 + 2.00t) N m. At time t = 1.00 s, its angular momentum is 5.00 kg.m2/s. What is...

Assist me please,,i am stuck 11 A study was conducted to investigate lengths of stay, in days, of short-term stay patients in a particular hospital. Independent random samples of 40 male patients and...

(Preferred stockholder expected return) You own 150 shares of Dalton Resources preferred stock, which currently sells for $47.35 per share and pays annual dividends of $4.75 per share. a. What is...

You are the CFO of a company that has a market capitalization of $20 billion. The firm has 50 million shares outstanding, so the shares are trading at $400 per share. You need to raise $1 billion and...