Given .

and

……… . (i)

Now,

So, (i) reduces to

So, locus of is circle whose center is ( ) and radius is 1.
Since, , we have following region traced by the locus of .

As shown in the figure the set S consists of the locus of units circles centered at a point on the line segment with end points at -2 and 2 on the Argand plane. Therefore, the area consists of the area of two semi circles and area of rectangle .
So, the required area is .

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