Point P represent the complex number z=x+iy and point Qrepresents the complex number z+1/z. If P moves on the circle |z|=2, then the eccentricity of locus of point Q is

Options

A. `3//5`
B. `4//5`
C. `3//4`
D. `1//2`

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
We have a point \( P \) represented by the complex number \( z = x + iy \) and a point \( Q \) represented by the complex number \( z + \frac{1}{z} \). The point \( P \) moves on the circle defined by \( |z| = 2 \).

### Step 2: Write the equation of the circle
Since \( |z| = 2 \), we can express this in terms of \( x \) and \( y \):
\[
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