Solve the system of equations `R e(z^2)=0,\ |z|=2`

Explanation

To solve the system of equations given by \( \text{Re}(z^2) = 0 \) and \( |z| = 2 \), we can follow these steps:

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

### Step 2: Use the modulus condition
From the condition \( |z| = 2 \), we have:
\[
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