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NDA 2020 Maths · Mathematics · Complex Numbers and Quadratic Equations · medium

If ω is a complex cube root of unity, then (1-ω+ω^2(1+ω-ω^2 equals

Single correct option

If ω\omega is a complex cube root of unity, then (1−ω+ω2)(1+ω−ω2)(1-\omega+\omega^2)(1+\omega-\omega^2) equals
  1. A. 4
  2. B. 0
  3. C. 1
  4. D. −4-4
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Answer: (A) 4

Use 1+ω2=−ω1+\omega^2=-\omega and 1+ω=−ω21+\omega=-\omega^2. Then 1−ω+ω2=−2ω1-\omega+\omega^2=-2\omega and 1+ω−ω2=−2ω21+\omega-\omega^2=-2\omega^2. The product is 4ω3=44\omega^3=4. Assuming each factor equals zero is the common error.
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Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake