If the point $z$ in the complex plane describes a circle with radius $2$ with centre at the origin then the point $z+\frac{1}{z}$ describe...
Options
A Circle
A parabola
an ellipse
a hyperbola
What I did... Did some elementary manipulations on the given term and conditions but couldn't really equate my manipulations to anything.
Putting $z=2e^{it}$ gives the $x$ and $y$ coordinates of the transformed shape as $x=(5/2)\cos t$ and $y=(3/2)\sin t$. These parametrise the ellipse $$\frac{x^2}{(5/2)^2}+\frac{y^2}{(3/2)^2}=1.$$