The complex number $z$ traces a circle centered at the origin with radius 2.  Then $z + \frac{1}{z}$ traces a:
(A) circle
(B) parabola
(C) ellipse
(D) hyperbola

Enter the letter of the correct option.
Question:
The complex number $z$ traces a circle centered at the origin with radius 2.  Then $z + \frac{1}{z}$ traces a:
(A) circle
(B) parabola
(C) ellipse
(D) hyperbola

Enter the letter of the correct option.
Answer:
Let's think step by step.

user
\text{(C)}
The complex number $z$ traces a circle centered at the origin with radius 2.  Then $z + \frac{1}{z}$ traces a:
(A) circle
(B) parabola
(C) ellipse
(D) hyperbola

Enter the letter of the correct option.
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