SATHEE: Complex Numbers 2 Question 27

Complex Numbers 2 Question 27

28.

Let $z$ be any point in $A \cap B \cap C$ and let $w$ be any point satisfying $| w - 2 - i | < 3$ . Then, $| z | - | w | + 3$ lies between

(a) -6 and 3

(b) -3 and 6

(d) -3 and 9

Passage II

Let $S = S_{1} \cap S_{2} \cap S_{3}$ , where

$S_{1} = z \in C : | z | < 4, S_{2} = z \in C : lm \frac{z - 1 + \sqrt{3} i}{1 - \sqrt{3} i} > 0$

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

(2008)

Show Answer

Answer:

Correct Answer: 28. (d)

Solution:

Since,

$| w - (2 + i) | < 3 \Rightarrow | w | - | 2 + i | < 3$

$\begin{array}{ll} \Rightarrow & - 3 + \sqrt{5} < | w | < 3 + \sqrt{5} \\ \Rightarrow & - 3 - \sqrt{5} < - | w | < 3 - \sqrt{5} \end{array}$

Also, $| z - (2 + i) | = 3$

$\begin{array}{ll} \Rightarrow & - 3 + \sqrt{5} \leq | z | \leq 3 + \sqrt{5} \\ ∴ & - 3 < | z | - | w | + 3 < 9 \end{array}$

Complex Numbers 2 Question 27

28.

Passage II

Answer:

Engineering Preparation

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Complex Numbers 2 Question 27

28.

Passage II

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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