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The locus of z which lies in shaded region (excluding the boundaries) is best represented by (2005S) 
  • a)
    z : |z + 1| > 2 and |arg (z+1)| < π/4
  • b)
    z : |z – 1| > 2 and |arg (z–1)| < π/4
  • c)
    z : |z + 1| < 2 and |arg (z+1)| < π/2
  • d)
    z : |z – 1| < 2 and |arg (z+1)| < π/2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The locus of z which lies in shaded region (excluding the boundaries) ...
Here we observe that.
AB = AC = AD = 2
∴ BCD is an arc of a circle with centre at A and radius 2.
Shaded region is outer (exterior) part of this sector ABCDA.
∴ For any pt. z on arc BCD we should have | z – (– 1) | = 2
and for shaded region, | z + 1| > 2 ....(i)
For shaded region we also have -p /4 < arg ( z + 1) <p /4
or | arg (z  + 1) | <p /4 ...(ii)
Combining (i) and (ii), (a)  is the correct option
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The locus of z which lies in shaded region (excluding the boundaries) is best represented by (2005S)a)z : |z + 1| > 2 and |arg (z+1)| < π/4b)z : |z – 1| > 2 and |arg (z–1)| < π/4c)z : |z + 1| < 2 and |arg (z+1)| < π/2d)z : |z – 1| < 2 and |arg (z+1)| < π/2Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The locus of z which lies in shaded region (excluding the boundaries) is best represented by (2005S)a)z : |z + 1| > 2 and |arg (z+1)| < π/4b)z : |z – 1| > 2 and |arg (z–1)| < π/4c)z : |z + 1| < 2 and |arg (z+1)| < π/2d)z : |z – 1| < 2 and |arg (z+1)| < π/2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The locus of z which lies in shaded region (excluding the boundaries) is best represented by (2005S)a)z : |z + 1| > 2 and |arg (z+1)| < π/4b)z : |z – 1| > 2 and |arg (z–1)| < π/4c)z : |z + 1| < 2 and |arg (z+1)| < π/2d)z : |z – 1| < 2 and |arg (z+1)| < π/2Correct answer is option 'A'. Can you explain this answer?.
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