Find the non-zero complex numbers `z` satisfying ` barz =i z^2dot`

Explanation

To solve the equation \( \bar{z} = i z^2 \) for non-zero complex numbers \( z \), we will follow these steps:

### Step 1: Express \( z \) in terms of its real and imaginary parts
Let \( z = x + iy \), where \( x \) and \( y \) are real numbers. The conjugate of \( z \) is given by:
\[ \bar{z} = x - iy \]

...