Solve the equation `|z|=z+1+2idot`

Explanation

To solve the equation \( |z| = z + 1 + 2i \), we will follow these steps:

### Step 1: Express \( z \) in terms of real and imaginary parts
Let \( z = x + iy \), where \( x \) is the real part and \( y \) is the imaginary part.

### Step 2: Write the modulus of \( z \)
The modulus of \( z \) is given by:
\[
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