Let the curve z(1+i)+ z(1-i)=4, z , divide the region |z-3| 1 into two parts of areas and . Then | - | equals :
(3) 1+ 2
z=x+iy: z(1+i)+ z(1-i)=2(x-y)=4 line x-y=2; disc: centre (3,0), radius 1
[figure]
Line meets the circle at (2,0) and (3,1) chord subtends 90 at the centre
= 14 (1)2- 12(1)(1)= 4- 12, = -
| - |= -2 =1+ 2
Answer: (3)
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