Let C be the set of all complex numbers- Let S1- z-z-3-2i-2-8 -S2- z-Rez - 5 and S3- z-z-z- 8-Then the number of elements in S1- S2- S3 is equal to

Clearly, S_1 is a circle of centre (3,2) and radius 2√(2) , S_2 nbsp;is plane with x≥ 5 and nbsp;S_3 is plane with y∈( ∞ , 4]∪ [4,∞ ) ∴ Only one point P i ...

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Byju's Answer

Standard XII

Mathematics

Geometrical Representation of Conjugate of a Complex Number

Let C be the ...

Question

Let $C$ be the set of all complex numbers. Let $S_{1} = {z \in C : | z - 3 - 2 i |^{2} = 8},$
$S_{2} = {z \in C : R e (z) \geq 5}$ and
$S_{3} = {z \in C : | z - ¯ z | \geq 8} .$
Then the number of elements in $S_{1} \cap S_{2} \cap S_{3}$ is equal to

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Solution

The correct option is B $1$
Clearly, $S_{1}$ is a circle of centre $(3, 2)$ and radius $2 \sqrt{2}$ ,
$S_{2}$ is plane with $x \geq 5$
and $S_{3}$ is plane with $y \in (- \infty, - 4] \cup [4, \infty)$

$∴$ Only one point $P$ is the solution.

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Similar questions

Q. Let

C

be the set of all complex numbers. Let

S_{1} = {z \in C : | z - 2 | \leq 1}

and

S_{2} = {z \in C : z (1 + i) + ¯ z (1 - i) \geq 4}

. Then the maximum value of

{∣ ∣ ∣ z - \frac{5}{2} ∣ ∣ ∣}^{2}

for

z \in S_{1} \cap S_{2}

is equal to

Q. Let

S_{1}, S_{2}

and

S_{3}

be three sets defined as

S_{1} = {z \in C : | z - 1 | \leq \sqrt{2}}

S_{2} = {z \in C : Re ((1 - i) z) \geq 1}

S_{3} = {z \in C : Im (z) \leq 1}

Then the set

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

Q. Let

C

be the set all complex number. Let

P = {z ϵ C : | z | = 1}

and

Q = {z ϵ C : z^{2} = 1}

. Then

Q. Let

S = S_{1} \cap S_{2} \cap S_{3},

where

S_{1} = {z ϵ C : | z | < 4}, S_{2} = {z ϵ C : I m [\frac{z - 1 + \sqrt{3} i}{1 - \sqrt{3} i}] > 0} a n d S_{3} = {z ϵ C : R e (z) > 0} .

Area of

S =

Q. Let

S = S_{1} \cap S_{2} \cap S_{3},

where

S_{1} = {z \in C : | z | < 4},

S_{2} = {z \in C : Im (\frac{z - 1 + \sqrt{3} i}{1 - \sqrt{3} i}) > 0}

and

S_{3} = {z \in C : Re z > 0}

Area of

S =

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Let C be the set of all complex numbers. Let S1={z∈C:|z−3−2i|2=8}, S2={z∈C:Re(z)≥5} and S3={z∈C:|z−¯z|≥8}. Then the number of elements in S1∩S2∩S3 is equal to

The correct option is B 1Clearly, S1 is a circle of centre (3,2) and radius 2√2 , S2 is plane with x≥5 and S3 is plane with y∈(−∞,−4]∪[4,∞) ∴ Only one point P is the solution.

Let $C$ be the set of all complex numbers. Let $S_{1} = {z \in C : | z - 3 - 2 i |^{2} = 8},$
$S_{2} = {z \in C : R e (z) \geq 5}$ and
$S_{3} = {z \in C : | z - ¯ z | \geq 8} .$
Then the number of elements in $S_{1} \cap S_{2} \cap S_{3}$ is equal to

The correct option is B $1$
Clearly, $S_{1}$ is a circle of centre $(3, 2)$ and radius $2 \sqrt{2}$ ,
$S_{2}$ is plane with $x \geq 5$
and $S_{3}$ is plane with $y \in (- \infty, - 4] \cup [4, \infty)$

$∴$ Only one point $P$ is the solution.