JEE Math Practice Question

Let $z$ be a complex number satisfying $|z|^{3}+2 z^{2}+4 \bar{z}-8=0$, where $\bar{z}$ 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. List-I (P) $|z|^{2}$ is equal to (Q) $|Z-\bar{Z}|^{2}$ is equal to (R) $|Z|^{2}+|Z+\bar{Z}|^{2}$ is equal to (S) $|z+1|^{2}$ is equal to List-II (1) 12 (2) 4 (3) 8 (4) 10 (5) 7 The correct option is:

1. A.$(P) \rightarrow(1) \quad(Q) \rightarrow(3) \quad(R) \rightarrow(5) \quad(S) \rightarrow$ (4)
2. B.$(P) \rightarrow(2) \quad(Q) \rightarrow(1) \quad(R) \rightarrow(3) \quad(S) \rightarrow(5)$
3. C.$(P) \rightarrow(2) \quad(Q) \rightarrow(4) \quad(R) \rightarrow(5) \quad(S) \rightarrow(1)$
4. D.$(P) \rightarrow(2) \quad(Q) \rightarrow(3) \quad(R) \rightarrow(5) \quad(S) \rightarrow(4)$