If complex number z=x +iy satisfies the equation `Re (z+1) = |z-1|`, then prove that z lies on `y^(2) = 4x`.

Explanation

To prove that the complex number \( z = x + iy \) satisfies the equation \( \text{Re}(z + 1) = |z - 1| \) and lies on the curve \( y^2 = 4x \), we will follow these steps:

### Step 1: Write the given equation
We start with the equation:
\[ \text{Re}(z + 1) = |z - 1| \]
Substituting \( z = x + iy \):
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