Need Help with some questions

[sunny123]

Hi I need help in solving the following equation. This question is Picked up from subject BCS12 Page 6. I have solved it on paper but I am not able to understand some logic. Please see the paper for further details.

 

[topsquark]

It seems that there is some information missing. If \(\displaystyle \omega\) is a (complex) cube root of -1 then we know that \(\displaystyle \omega ^2 + \omega + 1 = 0\).

-Dan

 

[sunny123]

Please check the attachment below, the rectangle

It seems that there is some information missing. If \(\displaystyle \omega\) is a (complex) cube root of -1 then we know that \(\displaystyle \omega ^2 + \omega + 1 = 0\).

-Dan

I was doing some research on google and I cam across same info that ω2+ω+1=0 so ω2+ω=-1. I think this proves it. ( I think the problem arose as We have not started cube root of Unity)

 

[topsquark]

Please check the attachment below, the rectangle


I was doing some research on google and I cam across same info that ω2+ω+1=0 so ω2+ω=-1. I think this proves it. ( I think the problem arose as We have not started cube root of Unity)

My main point here is that you didn't supply the whole problem...

-Dan

 

[sunny123]

My main point here is that you didn't supply the whole problem...

-Dan

Dan can you please explain, since my book gave me a question in the same manner. Like I have posted in first image. I was able to solve all of them except question (d) ( Which I was only able to solve partially) After you mentioned unity I googled it and found the reason for the answer. My main stream is not math, So this is new to me.

 

[topsquark]

Thank you. I see no reason why the solution manual (or instructor?) should have stated that \(\displaystyle \omega\) should be considered to be a cube root of -1. It is standard notation (sort of) but I see no reason why you would have applied it to this problem.

-Dan

 

[HallsofIvy]

At some point previously in the book, there must have been the statement that \(\displaystyle \omega\) would represent the principle cube root of -1.