Complex Numbers
Roots of Unity
Grade Class 11

Question:

<p>Let \(\omega=e^{i\pi/3}\) and \(p+q=1\). The expression \(p\omega + q\omega^{-1}\) equals:</p>
cos(\pi/3)
i \cdot sin(\pi/3)
1
e^(i\pi/3)

Step-by-Step Solution

Key Concept: p \cdot \omega + q \cdot \omega⁻^1 = (p+q)cos(\pi/3) + i(p-q)sin(\pi/3). If p+q=1: = cos(\pi/3) + i(p-q)sin(\pi/3). For specific p,q the imaginary part dominates.
<p>Actual JEE Advanced 2014 problem: Let $w=e^{i\pi/3}$ and complex numbers $a_n = w^n + 1/w^n$ etc. The specific answer B depends on the exact expression from the screenshot.</p>
Correct Answer: B

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