Let 
. Let Re(w) = 0 be the circle C of radius 1 in the first quadrant touching the line y = 1 and the y-axis. If the curve Im(w) = 0 intersects C at A and B, then 30 (AB) 2 is equal to ________ .
Text Solution
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Given,
And 
,
So, taking 
We get,
And, 
Now given 
circle is touching 
and y -axis, with radius 1 , so we have equation of circle
So, on comparing with 
we get,
So, on comparing with 
we get,
So, 
And given 
intersects the circle,
So, solving 
and 
we get,
Intersecting point as 
and 
Hence, by distance formula we get,
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