UrbanPro
Login Ask & Answer Success Stories Paid Courses Free Classes Tuition & Classes Fees Write a Review All Categories Help Center
Post your Learning Need Signup as a Tutor
✕

Popular Cities

Bangalore

Hyderabad

Delhi

Mumbai

Chennai

Pune

Kolkata

Gurgaon

Ahmedabad

Jaipur

Noida

✕

Take Class 12 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Book a Free Demo

Class 12 Tuition > Learn Class XI-XII Tuition (PUC) > Prove that sum of cube roots of unity is zero.
✕

Search in

Prove that sum of cube roots of unity is zero.

Asked by Last Modified  

6 Answers

Learn Class XI-XII Tuition (PUC)

Follow 2
Answer

Please enter your answer

We are mainly interested in the roots of unity; however, we begin by being general and presenting a theorem. The cyclotomic equation is: cyclotomic Where , n=2,3... and in the complex plane. And because it is not surprisingly, cyclotomic means 'related to the roots of unity' and often refers...
read more
We are mainly interested in the roots of unity; however, we begin by being general and presenting a theorem. The cyclotomic equation is: cyclotomic[1.01] Where [1.02], n=2,3... and in the complex plane. And because it is not surprisingly, cyclotomic means 'related to the roots of unity' and often refers to the equation: [1.03] The theorem is that the roots of cyclotomicare: [1.04] Where z and a are complex numbers, l=0,1,2, ... ,n-1, and ??read less
Comments
Dislike Bookmark

Maths Teacher

Cube roots of unity are 1, (-1+root 3i)/2 and (-1-root3i)/2. If you add all these you get zero.If you factorise x^3-1 yiy get (x-1) (x^2+x+1) . And the roots of tge second equation are complex as given above
Comments
Dislike Bookmark

Physics and Maths made easy

Write 1.0 = 1.0* Therefore (1.0)^(1/3) = 1.0 * for n={0,1,2} Therefore the cube roots are 1.0, (1/2) + i*sq root (3))/2, (-1/2)+ i*(- sq root (3))/2] sum of which three roots is + i * = 0+i*0
read more
Write 1.0 = 1.0*[cos(2*n*pi) + sin(2*n*pi)] Therefore (1.0)^(1/3) = 1.0 * [cos(2*n*pi/3)+sin(2*n*pi/3)] for n={0,1,2} Therefore the cube roots are 1.0, (1/2) + i*sq root (3))/2, (-1/2)+ i*(- sq root (3))/2] sum of which three roots is [1+(1/2)+(-1/2)] + i * [(sq root (3))/2 - (sq root (3))/2] = 0+i*0 read less
Comments
Dislike Bookmark

Mathematics

Consider an equation: z3-1=0 here three roots are : z1,z2,z3 then z3-1=0 z3=1 then we can easily solve z1=1, z2=w= (-1+i?3)/2, & z3=w2= (-1-i?3)/2 HERE WE CAN EASILY SOLVE THAT 1+Z2+Z3 =1+W+W2=1+ (-1+i?3)/2 + (-1-i?3)/2 =(2-1+i?3)/2 (-1-i?3)/...
read more
Consider an equation: z3-1=0 here three roots are : z1,z2,z3 then z3-1=0 z3=1 then we can easily solve z1=1, z2=w= (-1+i?3)/2, & z3=w2= (-1-i?3)/2 HERE WE CAN EASILY SOLVE THAT 1+Z2+Z3 =1+W+W2=1+ (-1+i?3)/2 + (-1-i?3)/2 =(2-1+i?3)/2 (-1-i?3)/ = 0 i.e. 1+w+w2=0 SO, sum of cube roots of unity is zero read less
Comments
Dislike Bookmark

SME in Mathematics & Statistics

To find roots of the equation x3 - 1 = 0 x3 - 1 = 0 (x - 1)(x2 + x + 1) = 0 Since x3 - 1 = 0 is a polynomial equation of degree 3, it will have three roots. We can see that one of the roots is 1. The other 2 roots are complex roots. Let one of them is w. Then it will satisfy the equation. (w -...
read more
To find roots of the equation x3 - 1 = 0 x3 - 1 = 0 (x - 1)(x2 + x + 1) = 0 Since x3 - 1 = 0 is a polynomial equation of degree 3, it will have three roots. We can see that one of the roots is 1. The other 2 roots are complex roots. Let one of them is w. Then it will satisfy the equation. (w - 1)(w2 + w + 1) = 0 w cannot be 1. Hence, w2 + w + 1 = 0 If w is a root, we can see that w2 is another root. Since, w2 + w + 1 = 0, we can say that sum of cube roots of unity is zero. read less
Comments
Dislike Bookmark

Teaching is my passion!!!!

1+w+w2=0
Comments
Dislike Bookmark

View 4 more Answers

Related Questions

Which is the recently discovered element?
Nihonium (Nh) , Moscovium (Mc), Tennessine (Ts) , Oganesson (Og).
Ayesha
Is there a guide to maths of XI and XII of IGCSE syllabus? It is because text book questions cannot be solved with clues taken only from their examples. Kindly guide. Thanks.
You can get MATHEMATICS revision guide by OXFORD PUBLISHERS
Kuruvila Daniel
The electric intensity at any point between two oppositely charged plain sheets is __________. (s/3Îo, s/Îo, s/2Îo, 2s/Îo)
s/Îo as Mr G says
Narendra Kumar
0 0
6
If the ratio of rates of diffusion of two gases is 4:3, then ratio of their molecular weights would be
Grahams law of diffusion
Ayan Arif
A and B toss a coin alternately till one of them gets a head and wins the game. if A starts first , find the probability that B will win the game.
U.k. Akshay posted a question in Class XI-XII Tuition (PUC) Question: A and B toss a coin alternately till one of them gets a head and wins the game. if A starts first , find the probability that B...
Kumar Upendra Akshay
2 0
6

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons

Find The Area Of Trapeziam ABCD
Question: Solution: Drop a perpendicular from C to AB 1/2 × 1/2 × 4 ×BC = 8 BC = 8sin 30° = 1/2 = h/ 4h = 2 Area => 1/ 2 × 2 = 14

Sujoy Das

2 0
0
Largest value of min (2 + x^2, 6 -3x) When x > 0
Question: Largest value of min (2 + x^2, 6 -3x) when x > 0. Solution: One is increasing function and other is decreasing. so their intersection is given by: 2+x^2 = 6-3x. x>0 so can't be -4....

Sujoy Das

2 0
0
Dissolution Of Partnership Firm - Questions
CHAPTER: 5 Q.1 Distinguish between dissolution of partnership and dissolution of partnership firm on the basis of continuation of business. Q.2 Why is Realisation Account prepared on dissolution of partnership...

Mahesh Kumar

1 0
0
Protein
Proteins are organic molecules consisting of many amino acids bonded together. Amino Acids: Monomers or building blocks of all proteins. Parts of the Amino Acid: a) Amino group (NH2) b) Carboxyl...

Bhakti M.

0 0
0
Business Studies Class XII - Case Studies
As per new pattern, questions based on case study can be asked in exam. These type of questions are introduced to check students ability to understand and apply his/her knowledge to given situation. Do...

Nidhi

0 0
0

Recommended Articles

Meet Raghunandan.G.H, a B. Tech Tutor from...

Raghunandan is a passionate teacher with a decade of teaching experience. Being a skilled trainer with extensive knowledge, he provides high-quality BTech, Class 10 and Class 12 tuition classes. His methods of teaching with real-time examples makes difficult topics simple to understand. He explains every concept in-detail...

Read full article >

Meet Urmila, an MBBS tutor from Bangalore

Urmila is a passionate teacher with over 8 years of experience in teaching. She is currently pursuing her Ph. D. She provides classes for Class 11, Class 12, MBBS and Medical tuition.  Urmila began her career in teaching long before she became a teacher. She used to provide classes for foreign national students in her college...

Read full article >

Meet Mohammad Wazid, a skilled trainer for...

Mohammad Wazid is a certified professional tutor for class 11 students. He has 6 years of teaching experience which he couples with an energetic attitude and a vision of making any subject easy for the students. Over the years he has developed skills with a capability of understanding the requirements of the students. This...

Read full article >

Meet Swati, a Hindi Tutor from Bangalore

Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...

Read full article >

Find PUC Tuition near you
PUC Tuition in Delhi
PUC Tuition in Bangalore
PUC Tuition in Hyderabad
PUC Tuition in Kolkata
PUC Tuition in Mumbai
PUC Tuition in Chennai
PUC Tuition in Pune
PUC Tuition in Jaipur
PUC Tuition in Lucknow
PUC Tuition in Noida
Online Tuition Class 12

Looking for Class 12 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you
X

Looking for Class 12 Tuition Classes?

The best tutors for Class 12 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 12 Tuition with the Best Tutors

The best Tutors for Class 12 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more

ThinkVidya Learning Pvt Ltd © 2010-2024All Rights Reserved