Let S = \z : 3 |2z - 3(1 + i)| 7 \ be a set of complex numbers. Then Minz S | (z + 12(5 + 3i) ) | is equal to :
(4) 32
3 |2z - 3(1 + i)| 7 32 |z - ( 32 + 32i ) | 72
S is the annulus with centre C ( 32, 32 ), radii 32 and 72.
|z + 12(5 + 3i) | = distance of z from P (- 52, - 32 )
CP = 42 + 32 = 5 > 72 P lies outside the outer circle
minimum distance = CP - 72 = 5 - 72 = 32
Answer: (4)
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