Paragraph: Let A, B, C be three sets of complex numbers as defined below. A=\ z ; lm z ≥ 1\ ; B=\ z:|z-2-i|=3\ ; C=\ z: Re((1-i) z)= 2 \ . Question: The number of elements in the set A B C is

Correct answer: B. 1 Let z=x+i y Set A corresponds to the region y ≥ 1 . Set B consists of points lying on the circle, centred at (2,1) and radius 3 , i.e., x^2+y^2-4 x-2 y=4 Set C consists of points lying on the x+y= 2 Clearly, there is only one point of intersection of the line x+y= 2 and circle x^2+y²-4 x-2 y=4 .

JEE Advanced 2008Paper 1

Exam: JEE Advanced
Year: 2008
Paper: Paper 1
Subject: Mathematics
Chapter: Complex Number

JEE Advanced 2008 · Paper 1 · Mathematics · Complex Number

Paragraph: Let A, B, C be three sets of complex numbers as defined...

Paragraph: Let

A, B, C

be three sets of complex numbers as defined below.

A=\{z ; \operatorname{lm} z \geq 1\} ; B=\{z:|z-2-i|=3\} ; C=\{z: \operatorname{Re}((1-i) z)=\sqrt{2}\}

.Question: The number of elements in the set

A \cap B \cap C

is $Paragraph: Let A, B, C be three sets of complex numbers as defined below. A=\ z ; lm z ≥ 1\ ; B=\ z:|z-2-i|=3\ ; C=\ z:$ $Paragraph: Let A, B, C be three sets of complex numbers as defined below. A=\ z ; lm z ≥ 1\ ; B=\ z:|z-2-i|=3\ ; C=\ z:$

Options

A0
B1
C2
D $\infty$

Correct answer

B. 1

Step-by-step solution

Let

z=x+i y

Set

A

corresponds to the region

y \geq 1

. Set

B

consists of points lying on the circle, centred at

(2,1)

and radius 3 , i.e.,

x^2+y^2-4 x-2 y=4\text{ Set }

\text{ consists of points lying on the }

x+y=

\sqrt{2}<img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fpyq%252Fjee_advanced%252F3NScNru6X2gqkLN9tmqN6mzwDUF8CODMBd5aCcEBqAU.original.fullsize.png%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_advanced%2F3NScNru6X2gqkLN9tmqN6mzwDUF8CODMBd5aCcEBqAU.original.fullsize.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_advanced%2F3NScNru6X2gqkLN9tmqN6mzwDUF8CODMBd5aCcEBqAU.original.fullsize.png?alt=media">

\\ Clearly, there is only one point of intersection of the line x+y=

\sqrt{2} \text{ and circle }

x^2+y²-4 x-2 y=4 .

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