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Complex Numbers question

2023 · 11 Apr · Shift 2 · Q26

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PYQ Library
JEE Main
Mathematics
Complex Numbers
2023 · 11 Apr · Shift 2 · Q26

Complex Numbers question

2023 · 11 Apr · Shift 2 · Q26

JEE MainMathematicsComplex NumbersMCQ+4 / −1

For

a \in \mathbb{C}

, let

\mathrm{A}=\{z \in \mathbb{C}: \operatorname{Re}(a+\bar{z}) \gt \operatorname{Im}(\bar{a}+z)\}

and

\mathrm{B}=\{z \in \mathbb{C}: \operatorname{Re}(a+\bar{z})(S1): If

\operatorname{Re}(a), \operatorname{Im}(a) > 0

, then the set A contains all the real numbers (S2) : If

\operatorname{Re}(a), \operatorname{Im}(a) < 0$$, then the set B contains all the real numbers,

A
both are false
B
only (S1) is true
C
only (S2) is true
D
both are true

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