SATHEE: Complex Numbers 4 Question 4

Complex Numbers 4 Question 4

4. The shaded region, where $P = (- 1, 0), Q = (- 1 + \sqrt{2}, \sqrt{2})$ $R = (- 1 + \sqrt{2}, - \sqrt{2}), S = (1, 0)$ is represented by $(2005, 1 M)$

(a) $| z + 1 | > 2, | \arg (z + 1) | < \frac{π}{4}$

(b) $| z + 1 | < 2, | \arg (z + 1) | < \frac{π}{2}$

(d) $| z - 1 | < 2, | \arg (z + 1) | > \frac{π}{2}$

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Answer:

Correct Answer: 4. (a)

Solution:

Since, $| P Q | = | P S | = | P R | = 2$

$∴$ Shaded part represents the external part of circle having centre $(- 1, 0)$ and radius 2 .

As we know equation of circle having centre $z_{0}$ and radius $r$ , is $| z - z_{0} | = r$

$\begin{array}{ll} ∴ & | z - (- 1 + 0 i) | > 2 \\ \Rightarrow & | z + 1 | > 2 \end{array}$

Also, argument of $z + 1$ with respect to positive direction of $X$ -axis is $π / 4$ .

$∴ \arg (z + 1) \leq \frac{π}{4}$

and argument of $z + 1$ in anticlockwise direction is $- π / 4$ .

$∴ \to π / 4 \leq \arg (z + 1)$

From Eqs. (i) and (ii),

$| \arg (z + 1) | \leq π / 4$

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Complex Numbers 4 Question 4

4. The shaded region, where $P = (- 1, 0), Q = (- 1 + \sqrt{2}, \sqrt{2})$ $R = (- 1 + \sqrt{2}, - \sqrt{2}), S = (1, 0)$ is represented by $(2005, 1 M)$

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Complex Numbers 4 Question 4

4. The shaded region, where P=(−1,0),Q=(−1+2,2) R=(−1+2,−2),S=(1,0) is represented by (2005,1M)

Answer:

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चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

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4. The shaded region, where $P = (- 1, 0), Q = (- 1 + \sqrt{2}, \sqrt{2})$ $R = (- 1 + \sqrt{2}, - \sqrt{2}), S = (1, 0)$ is represented by $(2005, 1 M)$