For all $z \in C$ on the curve $C_{1}:|z|=4$, let the locus of the point $z+\frac{1}{z}$ be the curve $\mathrm{C}_{2}$. Then :

Question

the curves $C_{1}$ and $C_{2}$ intersect at 4 points

the curve $C_{2}$ lies inside $C_{1}$

the curve $C_{1}$ lies inside $C_{2}$

the curves $C_{1}$ and $C_{2}$ intersect at 2 points

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