QJEEM21Ma862b: JEE Main 2021 Mathematics - Class 11 JEEM21Ma862b Solution: Let C be the set of all complex numbers. Let S 1 = { z ∈ C

Question

Verified Solution • 2025–26 Session moderate

Let C be the set of all complex numbers. Let

S_{1} = {z \in C | | z - 3 - 2 i |^{2} = 8}

S_{2} = {z \in C | Re (z) \geq 5}

and

S_{3} = {z \in C | | z - \overset{―}{z} | \geq 8}

.

Then the number of elements in

S_{1} \cap S_{2} \cap S_{3}

is equal to :

Accepted Answer

S_{1} : | z - 3 - 2 i |^{2} = 8

| z - 3 - 2 i | = 2 \sqrt{2}

(x - 3)^{2} + (y - 2)^{2} = (2 \sqrt{2})^{2}

S_{2} : x \geq 5

S_{3} : | z - \overset{―}{z} | \geq 8

| 2 i y | \geq 8

2 | y | \geq 8

∴

y \geq 4

,

y \leq - 4

n (S_{1} \cap S_{2} \cap S_{3}) = 1

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