0

Guest

Courses New

If 1, w and w^2 is cube root of unity then show (1-w+w^2)(1-w^2+w^4)(1-w^4+w^8)......to n factors=2^2n.

If 1, w and w^2 is cube root of unity then show (1-w+w^2)(1-w^2+w^4)(1-w^4+w^8)......to n factors=2^2n.

Grade:11

1 Answers

Shailendra Kumar Sharma
188 Points
6 years ago
as we know 1-w+w2= 0
so 1+w2 =-w, so it will be -2w
take 1-w2+w4
=1-w2+w3*w=1-w2+w
(-w2-w2)=-2w2

Next term is 1-w4+w8 =( 1-w+w2)
so the trend will repeat 
Now (1-w+w2)X1-w2+w4 =(-2w)*(-2w2) =2^2
similarly for n terms it will be 2^2n

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More