If the points \( A(z), B(-z), C(1-z) \) are the vertices of an equilateral triangle \( \mathrm{A...
If the points \( A(z), B(-z), C(1-z) \) are the vertices of an equilateral triangle \( \mathrm{ABC} \), then \( \operatorname{Re}(z) \) is
(a) \( \frac{1}{4} \)
(b) \( \frac{\sqrt{3}}{2} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{\sqrt{2}} \)
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