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?

• A. $\left|z+\frac{1}{2}\right| \leq \frac{1}{2}$ for all $z \in S$
• B. $|z| \leq 2$ for all $z \in S$
• C. $\left|z+\frac{1}{2}\right| \geq \frac{1}{2}$ for all $z \in S$
• D. The set $S$ has exactly four elements

Answer 1

Answer: (B), (C)

$|z| \leq 2$ for all $z \in S$

Answer 2

(B) $|z| \leq 2$ for all $z \in S$
(C) $\left|z+\frac{1}{2}\right| \geq \frac{1}{2}$ for all $z \in S$