Q.

The number of points in the complex plane that satisfying the conditions |z−2|=2 , z(1−i)+z¯(1+i)=4 , (where i=−1 ) is:

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a

0

b

1

c

2

d

More than 2

answer is C.

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Detailed Solution

∵       Centre of the circle |z−2|=2 is   ( 2,0) and it lies on  z(1−i)+z¯(1+i)=4 .Hence, given line z(1−i)+z¯(1+i)=4  pass through the center of the circle, i.e., intersect at two points.∴   Number of solutions =2.
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