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The locus of point z satisfying R e(1/z)...

The locus of point `z` satisfying `R e(1/z)=k ,w h e r ek` is a nonzero real number, is a. a straight line b. a circle c. an ellipse d. a hyperbola

A

a straight line

B

a circle

C

an ellipse

D

a hyperbola

Text Solution

Verified by Experts

The correct Answer is:
B
Let `z=z+iy`. Then, `1/z=x/(x^(2)+y^(2))-(iy)/(x^(2)+y^(2))`
`therefore "Re"(1/z)=k`
`rArr x/(x^(2)+y^(2))=k rArr x^(2)+y^(2)-1/kx=0`, which is a circle.
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