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Question

If Re(1z)>12 and Re(z)>0, then which of the following is/are true about the locus of z?

A
The locus of z is the region inside a circle.
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B
The locus of z is the region inside an ellipse.
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C
Area of locus is π sq. units
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D
Centre of the locus is (1,0)
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Solution

The correct option is D Centre of the locus is (1,0)
Let z=x+iy
1z=1x+iy1z=xiyx2+y2

As Re(1z)>12, so
xx2+y2>122x>x2+y2x2+y22x<0(x1)2+y2<1

It's the interior region of the circle with centre (1,0) and the radius is 1 unit
Area is less than π sq. units

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