Question

The curve represented by the equation Re($\frac{1}{z}$) = 2 is:

• A. Circle with centre (1/4, 0)
• B. Straight line through (1/2, 0)
• C. Ellipse
• D. None of these

Answer 1

The correct option is A

Circle with centre (1/4, 0)

Re($\frac{1}{z}$) = Re$⟮\frac{x-iy}{x^2+y^2}⟯$ = 2 $\Rightarrow x^2+y^2-\frac{x}{2}$ = 0

$\therefore$ the curve is a circle with centre ($\frac{1}{4},0$)