Explanation

(b)
Given, $Re\ \left( \frac{1}{z} \right) = k\ \ \Rightarrow \ \ \ Re\left( \frac{1}{x + iy} \right) = k$
$\Rightarrow \ \ \ \ \ \ \ Re\left( \frac{x}{x^{2} + y^{2}} - \frac{iy}{x^{2} + y^{2}} \right) = k$
$\Rightarrow \ \ \ \ k = \frac{x}{x^{2} + y^{2}}$
$\Rightarrow \ \ \ x^{2} + y^{2} - \frac{1}{k}x = 0$
Which is an equation of circle.