If `omega` is a cube root of unity, then
`omega^(3)`= ……

Answer

To solve the problem, we need to determine what \( \omega^3 \) is, given that \( \omega \) is a cube root of unity.

### Step-by-Step Solution:

1. **Understanding Cube Roots of Unity**:
The cube roots of unity are the solutions to the equation \( x^3 = 1 \). These solutions are:
- \( 1 \)
- \( \omega \)
- \( \omega^2 \)

2. **Properties of Cube Roots of Unity**:
One important property of the cube roots of unity is that:
\[ 1 + \omega + \omega^2 = 0 \]
This means that \( \omega + \omega^2 = -1 \).

3. **Finding \( \omega^3 \)**:
By the definition of cube roots of unity, we have:
\[ \omega^3 = 1 \]
This is because \( \omega \) is defined as a cube root of unity, meaning when raised to the power of 3, it equals 1.

4. **Verification**:
To verify, we can multiply \( \omega \) by itself three times:
\[ \omega \cdot \omega \cdot \omega = \omega^3 = 1 \]
This confirms that \( \omega^3 = 1 \).

### Final Answer:
Thus, we conclude that:
\[ \omega^3 = 1 \]