(Hi),

If 1, Ω, Ω^2 are the cube roots of unity, find the value of:

1)Ω^2 + Ω^3 + Ω^4:

Ans:

Since Ω^3 = 1

Ω^2 + 1 + Ω

So, Ω^2 + Ω^3 + Ω^4 = 0

I did not understand how the final answer result to be a0.

Printable View

- September 1st 2009, 12:21 AMsaberteethCube Roots Of Unity (Quadratic Equations)
(Hi),

If 1, Ω, Ω^2 are the cube roots of unity, find the value of:

1)**Ω^2 + Ω^3 + Ω^4:**

**Ans:**

Since Ω^3 = 1

Ω^2 + 1 + Ω

So, Ω^2 + Ω^3 + Ω^4 = 0

I did not understand how the final answer result to be a**0**. - September 1st 2009, 12:39 AMBruno J.
Cube roots of unity are the roots of . Note that . Since is not a root of it must be a root of .

Now just notice that . - September 1st 2009, 02:30 AMsaberteeth
- September 1st 2009, 08:42 AMBruno J.
It's not always equal to zero, no. For instance it's equal to 3 when . However it's equal to 0 when is a cube root of unity, so is right! (Rock)

- September 1st 2009, 07:55 PMsaberteeth