For two non-zero complex numbers $z_{1}$ and $z_{2}$, if $\operatorname{Re}(z_{1}z_{2})=0$ and $\operatorname{Re}(z_{1}+z_{2})=0$, then which of the following are possible? A. $\operatorname{Im}(z_{1})>0$ and $\operatorname{Im}(z_{2})>0$ B. $\operatorname{Im}(z_{1})<0$ and $\operatorname{Im}(z_{2})>0$ C. $\operatorname{Im}(z_{1})>0$ and $\operatorname{Im}(z_{2})<0$ D. $\operatorname{Im}(z_{1})<0$ and $\operatorname{Im}(z_{2})<0$ Choose the correct answer from the options given below: