Solve the equation `z^2= barz`

Explanation

To solve the equation \( z^2 = \bar{z} \), we will follow these steps:

### Step 1: Express \( z \) in terms of \( x \) and \( y \)
Assume \( z = x + iy \), where \( x \) and \( y \) are real numbers.

### Step 2: Calculate \( z^2 \) and \( \bar{z} \)
- \( z^2 = (x + iy)^2 = x^2 + 2xyi - y^2 = x^2 - y^2 + 2xyi \)
- \( \bar{z} = x - iy \)
...