The locus of z which lies in shaded region (excluding the boundaries) is best represented by [2005]

Question

The locus of $z$ which lies in shaded region (excluding the boundaries) is best represented by [2005]

Smart Achievers · Accepted Answer

(1)

$In the figure, we see that$

$A B = A C = A D = 2$

$∴$ $B C D is an arc of a circle with centre at A and radius 2 . Shaded region is exterior part of this sector A B C D A .$

$∴$ $For any point represented by z on arc B C D we should have$

$| z - (- 1) |$ $= 2$

$and for shaded region, | z + 1 | > 2 . . . (i)$

$For shaded region, we also have$

$- \frac{π}{4} < \arg (z + 1) < \frac{π}{4}$

$or | \arg (z + 1) | < \frac{π}{4} . . . (i i)$

$From (i) and (ii), we get (1) is the correct option.$

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