Question: If 1, a 1 , a 2 ,a n-1 are the nth roots of unity, then the value of (1-a 1 ) (1 a

If 1, a1, a2,…an-1 are the nth roots of unity, then the value of (1-a1) (1 – a2)(1 – a3)…(1 – an-1) is

(a) ?3

(b) 1/2

(c) n

(d) 0

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

The detailed answer for the above question is provided ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

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

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Draw a graph that has the given adjacency matrix. 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0

Q:

The 50-kg glass tabletop rests on the centrally located equilateral triangular frame which is supported by three legs. Determine the smallest vertical force P that, when applied to the glass, would...

Q:

Does the set of the nth roots of unity [Eq. (1.36)] with the rule of combination being ordinary multiplication form a group? Justify your answer.

Q:

In general, an nth root of unit f is called primitive if all the nth roots of unity are obtained by raising it to successive powers: 1, , 2, 3, .... (a) Find all primitive (i) Fourth (ii) Fifth (iii)...

Q:

The discrete Fourier transform (DFT) and the fast Fourier transform (FFT) are possibly the two most important transforms you will ever see. All modern telecommunications relies on the FFT, as does...

Q:

Show that for a finite group, every refinement of a subnormal series with abelian quotients also has abelian quotients, thus completing the proof of Lemma 56.3. Data from Lemma 56.3 Let F be a field...

Q:

Treasury shares and their effects on performance ratios. Exhibit 14.14 presents the changes in common shareholders' equity of Monk Corporation for 2006 through 2008. Monk regularly purchases shares...

Q:

Two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls. Suppose that we win $2 for each black ball selected and we lose $1 for each white ball selected. Let X...

Q:

Use the MPG data to create a regression model to predict MPG from Speed and Displacement: MPG = 0 + 1( Speed) + 2( Displacement). a. What are the regression equation and R2 value? b. Look at residual...

Q:

Long-Term Behavior of Solutions: Suppose that r1 and r2 are the characteristic roots for ay" + by' + cy = 0, so the solution is y(t) = c1er1t. For Problems 1-2, discuss the long-term solution...

Q:

Consider a hollow 7075-T6 aluminum alloy circular tube. Consider the inside diameter as 150mm, outside diameter as 200mm and length as 8m. If one end of the pipe is free and the other is fixed,...

Q:

Would you consider the completion of the first hardware phase a milestone or a phase-gate review?

Q:

Consider the following theorem. Theorem If f is integrable on a , b , then a b f ( x ) d x = lim n i = 1 n f ( x i ) x where x = b - a n and x i = a i x Use the given theorem to evaluate the definite...

Q:

HASF Builders need to acquire the use of a construction machinery for construction business and are considering buying or leasing a machinery. The construction machine costs Rs. 10 Million and is...

Q:

Amass published a monthly newsletter for retail marketing managers and requires its subscribers to pay $75 in advance for a one year subscription. During the month of September 2013, Amass sold 200...

Q:

Maitea has decided to contribute to a savings program. She can open a traditional 401(k) or a Roth 401(k). She has determined that she can afford a $15, 600 contribution. Maitea's salary is $130, 500...

Q:

Find x2 n mahix - i it in WSs. Pry = 2 113 0U 7% 22 2 12 018 ab 1.2 x* x XX 2. 019

Q:

run another hypothesis test using this scenario: A town official claims that the average vehicle in their area sells for under the 80th percentile of your classmate's data set. Conduct a four-step...

Q:

Two different plasma etchers in a semiconductor factory have the same mean etch rate . However, machine 1 is newer than machine 2 and consequently has smaller variability in etch rate. We know that...

Q:

The problem for finding a largest block is described in Programming Exercise 8.35. Design a dynamic programming algorithm for solving this problem in O(n2) time. Write a test program that displays a...

Q:

My code is encountering an error: Traceback (most recent call last): File "main.py", line 18, in age = int(record[1]) IndexError: string index out of range The code an assignment are below: file=...

Q:

Complete class diagram (phase 5 and 6). 17 Questions. 17 To be submitted: 18 Marking Criteria. 20 Appendix A: Sample Output for a completed phase 6. 22 Objectives In this assignment you will develop...

Q:

Write A Separate Logging Decorator That Saves All Function Calls And Their Results In The File \"Log.Txt\". This Requires Opening The File For Appending: Logfile = Open('Log.Txt', 'A') You Will Need...

Q:

Treatment Opt1 Opt2 Opt3 Opt4 Opt5 Opt6 Opt7 Opt1 Opt2 Opt3 Opt4 Opt5 Opt6 Opt7 GIT_1-3 GIT_4-6 Ttest 0 -2 -3 -3 3 1 -3 -2 Opt1 1 1.984467 0 -2 -3 -2 3 -3 -3 0 Opt2 0.392254 1 0.038632 0 -3 -3 -3 3...