Question

Help !

Answer 1

\[\Huge (1+ \omega^2-\omega)((1-\omega^2+\omega)=?\]

Answer 2

\( 1,\omega,\omega^2\) are cube roots of unity.

Answer 3

@ganeshie8 @hartnn

Answer 4

use : \(1 + \omega + \omega^2 = 0\)

Answer 5

expression becomes :-
\((-2\omega)(-2\omega^2)\)

Answer 6

how did you apply that property?i died to apply it

Answer 7

did u open the brackets and get that?

Answer 8

\(\Huge (\color{red}{1+ \omega^2}-\omega)((\color{red}{1}-\omega^2+\color{red}{\omega})=?\)

Answer 9

substitute them

Answer 10

without opening? O_O

Answer 11

\(\Huge (\color{red}{1+ \omega^2}-\omega)((\color{red}{1}-\omega^2+\color{red}{\omega})=?\)


\(\Huge (\color{red}{-\omega}-\omega)((\color{red}{-\omega^2}-\omega^2)=?\)

Answer 12

clear right ?

Answer 13

i opened the brackets
\[\LARGE \cancel 1-\omega^2+\cancel \omega+\cancel \omega^2-\omega^4+\omega^3-\omega+\omega^3-\omega^2\]
\[-2 \omega^2+2\omega^3-\omega^4-\omega\]

Answer 14

uve complicated it :)

simplify further... u should get 4

Answer 15

use this : \(\omega^3 = 1\)

Answer 16

\[−2ω^2+2−ω^4−ω\]

Answer 17

\(\large −2ω^2+2−ω^{3+1}−ω \)

Answer 18

\[\[\Huge −2ω^2+2−2ω=>2(1-\omega-\omega^2)\]\]

Answer 19

Alright,

\(\Huge 2(1-(\omega+\omega^2) )\)

Answer 20

what now?

Answer 21

\(1+\omega + \omega^2 = 0 => \omega + \omega^2 = ?\)

Answer 22

finally 4 :P

Answer 23

im glad we finished lol

Answer 24

how was this an observation based question for you?

Answer 25

it was supposed to be a two line solution :)

Answer 26

??

Answer 27

dont expand the product.
stare at the given product for few secs

Answer 28

\(\Huge (\color{red}{1+ \omega^2}-\omega)((\color{red}{1}-\omega^2+\color{red}{\omega})=? \)

Answer 29

in the first factor,
u can replace that red thing wid a \(-\omega\)

Answer 30

in the second factor,
u can replace that red thing wid a \(-\omega^2\)

Answer 31

oh i see thanks :O

Answer 32

badiya tha

Answer 33

np :) happens when u study too much... we dont see simple things :o

Answer 34

:)

Answer 35

i didn't study complex no. yet this was my 1st question on application of that property..i just knew some properties..this one,w^3=1 and so so..i was just seeing a paper so saw this,wont forget now :D

Answer 36

ohkie :)
this video is bit weird... but it should be good enough if u starting it fresh :-
http://www.youtube.com/watch?v=3CXveDizmyc

Answer 37

i am not doing complex no. atm,was just trying to solve it :P no time to do it..boards over head

Answer 38

cant do a new chapter now is what i meant,ill see all this in march,added to playlist :D

Answer 39

okay, still u should knw why \(1 + \omega + \omega^2 = 0 \) and \(\omega^3 = 1\)
that short video can help u derive above two quickly...

it wont take more than 10 minutes for it to make sense for u

Answer 40

forget it, ugh i gave the wrong link, here is the correct one :-
http://www.youtube.com/watch?v=6PoKNHdfdqw