If z = x + iy lies in the third quadrant, then prove that `(barz)/(z)` also lies in the third quadrant when `y lt x lt 0`

Explanation

To prove that \(\frac{\bar{z}}{z}\) lies in the third quadrant when \(z = x + iy\) lies in the third quadrant and \(y < x < 0\), we will follow these steps:

### Step 1: Define the complex number and its conjugate
Let \(z = x + iy\), where \(x < 0\) and \(y < 0\) (since \(z\) is in the third quadrant). The conjugate of \(z\) is given by:
\[ \bar{z} = x - iy \]

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