Question

The locus of point z satisfying $Re\left(\frac{1}{z}\right)=k$, where $k$ is a nonzero real number, is

• A. A straight line
• B. A circle
• C. An ellipse
• D. A hyperbola

Answer 1

The correct option is B A circle

$Re\left(\frac{1}{z}\right)=\frac{x}{x^2+y^2}$
$\therefore x^2+y^2=\frac{x}{k}$
which is a circle