Question:
Let $S$ be the set of all complex numbers $z$ satisfying $\left|z^{2}+z+1\right|=1$. Then which of the following statements is/are TRUE?
Let $S$ be the set of all complex numbers $z$ satisfying $\left|z^{2}+z+1\right|=1$. Then which of the following statements is/are TRUE?
Updated On: Jul 9, 2024
- $\left|z+\frac{1}{2}\right| \leq \frac{1}{2}$ for all $z \in S$
- $|z| \leq 2$ for all $z \in S$
- $\left|z+\frac{1}{2}\right| \geq \frac{1}{2}$ for all $z \in S$
- The set $S$ has exactly four elements
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The Correct Option is B, C
Solution and Explanation
(B) $|z| \leq 2$ for all $z \in S$
(C) $\left|z+\frac{1}{2}\right| \geq \frac{1}{2}$ for all $z \in S$
(C) $\left|z+\frac{1}{2}\right| \geq \frac{1}{2}$ for all $z \in S$
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