Algebra

ronnie's Avatar
Scorching goIITian

Joined: 18 Feb 2012
Post: 264
2 Apr 2012 15:13:50 IST
2 People liked this
4
370 View Post
'COMPLEX' complex no....
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

x=w^2009^2009^2009.......2009 times..... then 1+x+x3=??? w is cube root of unity



Comments (4)


New kid on the Block

Joined: 10 Feb 2012
Posts: 1
2 Apr 2012 15:17:51 IST
0 people liked this

1

Blazing goIITian

Joined: 21 Mar 2012
Posts: 1457
2 Apr 2012 15:29:21 IST
0 people liked this

it is 0
hemang's Avatar

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
3 Apr 2012 10:34:47 IST
1 people liked this

see, 2009 is 2(mod 3).

and we raise it to an odd power,

2(mod 3) remains the same.

lemma -

2^(2n-1) is 2(mod 3) for all natural numbers , n.

4^n - 2 ,

(3+1)^n - 2.

(multiple of 3) - 1.

which is 2(mod 3). :)

so x = w^(power that is 2(mod3)).

x = w^2.

we want 1 + x + x^3 = 1 + w^2 + w^6 = 2 + w^2 = 1 + 1 + w + w^2 - w = 1 - w.

 

not sure. ;(

 

kartikAIR1's Avatar

Blazing goIITian

Joined: 2 Mar 2012
Posts: 308
3 Apr 2012 11:41:00 IST
1 people liked this

I agree with hemang !! x = w^2 !! sure..



Quick Reply


Reply

Some HTML allowed.
Keep your comments above the belt or risk having them deleted.
Signup for a avatar to have your pictures show up by your comment
If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team
Free Sign Up!
Sponsored Ads

Preparing for JEE?

Kickstart your preparation with new improved study material - Books & Online Test Series for JEE 2014/ 2015


@ INR 5,443/-

For Quick Info

Name

Mobile

E-mail

City

Class

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
Altitude - 16545 m
Post - 7958
2. Himanshu
Altitude - 10925 m
Post - 3836
3. Hari Shankar
Altitude - 10085 m
Post - 2217
4. edison
Altitude - 10825 m
Post - 7804
5. Sagar Saxena
Altitude - 8635 m
Post - 8064
6. Yagyadutt Mishr..
Altitude - 6330 m
Post - 1958

Find Posts by Topics

Physics

Topics

Mathematics

Chemistry

Biology

Parents Corner

Board

Fun Zone