Let \( z \) be a complex number satisfying \( |z|^3+2z^2+4\overline{z}-8=0 \), where \( \overline{z} \) denotes the complex conjugate of \( z \). Let the imaginary part of \( z \) be nonzero.
Match each entry in List-I to the correct entries in List-II.

The correct option is: