# complex vector q (1 Viewer)

#### Hikari Clover

##### Member

oh~~
i was stuck with that Q as well~~

from part 1 , u got r - a =XXXXXX
and then u just have to find another expression which involves r and b, divided equation 1 by ur second equation , hopefully u will get the answer....

#### Tmer

##### New Member
ah thank you so much, im gonna try that now, also can u do q6 part c, im having trouble... these questions are stressing me out now...

#### Hikari Clover

##### Member

i have to admit that i cant do ~~~~~~

sorry , cant help~~~

#### YannY

##### Member
ok heres how you do the question...
you know the cube roots of unity for 1+w+w^2=0

Now this also forms the vertices of an equilateral triange.

so you can see now that alpha, beta and phi are also these vertices if you let them be free vectors.

since 1, w and w^2 are the roots or vertices, we can equate alpha = 1, beta = w and phi = w^2.

the problem is alpha^2+beta^2+phi^2 = Alpha beta + beta phi + alpha phi

therefore : 1^2 + w^2 + (w^2)^2 = 1w + w(w^2) + 1w^2 (1)

note that in cube roots of unity w^3 = 1, w^4 = w etc.

therefore continuing with equation 1;

LHS: 1+w^2+w^4
= 1 + w + w^2
= 0
RHS = w + w^3 + w^2
= 1 + w + w^2
= 0
= LHS

Of course there might be other ways to hit this question but you can use this.
Anyways im up for a challenge of hard 3u maths and 4u maths stuff so please send me an email of your question if you got a hard one and i shall send you the document of it hand written scanned on comp, so its easier to read. email is silveroak555@hotmail.com hope we'll get this together

PS: dont send me anything more than complex and graphing till the next term cause i havent done them haha. oh and w = omega in the question. and no im not some 4eye asian nerd who looks like hes gonna break but i am asian so yeah.

#### tambourine

##### Member
Ok that paper looked really hard!!!

If I can't do that I'm failing my first assignment

#### SoulSearcher

##### Active Member
tambourine said:
Ok that paper looked really hard!!!

If I can't do that I'm failing my first assignment
Trust me, the paper will become easier once you have done more work in extension 2 maths and get exposed to more of these sorts of questions