SOLUTION: {{{w^3=1}}}, Find the exact values of {{{(1+2w+3w^2)}}} & {{{(1+3w+2w^2)}}}, given that these are roots of the eq'n {{{x^2 + 3x +3=0}. I did the Q, however I am just stuck on say

No complex imaginary number can be said to be "larger" or "smaller" than any
other complex numbers.  Only real numbers can be said to be larger or smaller
than other real numbers.  

We should do all the possibilities.

The problem from the very beginning:

Since 
 

and



are roots of the equation 



their sum is equal to the coefficient of x with the opposite sign:

So:



or






[We can check that their product will be the constant term 3, but
we don't need that.

(1) When we substitute 



into 

 

we get



-----

(2)  When we substitute 



into 

 

we get



------

(3) When we substitute 



into 

 

we get the value



------

(4) When we substitute 



into 

 

we get the value



---

So, the exact values of both   and , 
given that

 

and



are roots of the equation



Note that for , the sign of the imaginary part is
OPPOSITE the sign of the imaginary part of what is substituted, and
that for , the sign of the imaginary part is the 
SAME AS the sign of the imaginary part of what is substituted.

Edwin