Question

locus of point z satisfying Re(1/z)=k where k is non zero real number

Answer 1

z = x + i y
Re(1/z) = x/(x^2+y^2) = k
so k x^2 - x + k y ^2 = 0
(x - 1/2k)^2 + y^2 = 1/ 4k^2

This is a circle with radius 1/2k and center (1/2k, 0).

Answer 2

Answer:

(1/2k, 0)

Step-by-step explanation:

Given,

Re(1/z)=k where k is non zero real number.

To Find,

The locus of point z.

z = x + i y

Re(1/z) = x/(x^2+y^2) = k

so k x^2 - x + k y ^2 = 0

(x - 1/2k)^2 + y^2 = 1/ 4k^2

This is a circle with radius 1/2k and center (1/2k, 0).

#SPJ2