Question:medium
Let \(z_{1} = \frac{1}{2} +i\frac{\sqrt{3}}{2}\) and \(z_{2} = -\frac{1}{2} -i\frac{\sqrt{3}}{2}\) . If \(w = z_{1} + \bar{z}_{2}\) , then \(\overline{w} =\)
Let \(z_{1} = \frac{1}{2} +i\frac{\sqrt{3}}{2}\) and \(z_{2} = -\frac{1}{2} -i\frac{\sqrt{3}}{2}\) . If \(w = z_{1} + \bar{z}_{2}\) , then \(\overline{w} =\)
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\(z_1\) and \(z_2\) are cube roots of unity: \(z_1 = e^{i\pi/3}, z_2 = e^{-i2\pi/3}\). Their sum with conjugate may simplify.
Updated On: Apr 25, 2026
- 1
- \(\sqrt{3}\)
- \(i\sqrt{3}\)
- \(-i\sqrt{3}\)
- \(-\sqrt{3}\)
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The Correct Option is D
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