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Q.

P  is a point  satisfying  arg   z=π/4 , such that  sum  of its  distance  from two  given  points (0,1)  and (0,2) is minimum, then  p must  be   k3(1+i) .Then numerical  value of  k is --------

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answer is 2.

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Detailed Solution

PA+PB  will  be minimum 
Where  A and A’  are  mirror  image
A’ ,P,B  are  collinear 
Equation  of  line  A’B : 2x+y=2
Solve  A’B with y=x
 x=23,y=23
k=2

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