Mathematics

Mathematics

Problem

Let SS be the set of all complex number zz satisfying ∣z2+z+1∣=1|z^2 + z + 1| = 1 . Then, which of the following statement(s) is(are) TRUE? (A) ∣z+12∣≤12,∀z∈S|z + \frac{1}{2}| \leq \frac{1}{2}, \forall z \in S (B) ∣z∣≤2,∀z∈S|z| \leq 2, \forall z \in S . (C) ∣z+12∣>12,∀z∈S|z + \frac{1}{2}| > \frac{1}{2}, \forall z \in S (D) The set SS has exactly four elements

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