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Complex Numbers question

2020 · Shift 1 · Q27

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2020 · Shift 1 · Q27

Complex Numbers question

2020 · Shift 1 · Q27

JEE AdvancedMathematicsComplex NumbersMultiple correct+4 / −2

Let S be the set of all complex numbers z satisfying |z2 + z + 1| = 1. Then which of the following statements is/are TRUE?

A
$\left| {z + {1 \over 2}} \right|$ $\le {{1 \over 2}}$ for all z $\in$ S
B
|z| $\le$ 2 for all z $\in$ S
C
$\left| {z + {1 \over 2}} \right|\, \ge {1 \over 2}$ for all z $\in$ S
D
The set S has exactly four elements

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