If is a complex cube root of unity, what is the value of ?

Answer and explanation

Correct answer: C. 4

  1. Step 1: Use identity , so and .
  2. Step 2: First factor: .
  3. Step 3: Second factor: .
  4. Step 4: Multiply factors: . Since , the product is .
Answer
4.
Why not the others: '1' overlooks the factor of 2 in each bracket; '-1' makes a sign error in ; '0' incorrectly assumes one of the brackets vanishes.

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If omega is a complex cube root of… | Thanawiya Amma (Egypt)