So indeed, \( (z^2 + 2)^2 = 0 \), so roots are \( z = \pm i\sqrt2 \), each with multiplicity 2. But the **set of distinct roots** is still two: \( i\sqrt2, -i\sqrt2 \), each included twice. But the problem asks for **the sum of the real parts of all complex numbers \( z \)** satisfying the equation. Since real part is 0 for each, even with multiplicity, the sum is still \( 0 + 0 = 0 \). - go-checkin.com