JEE Math Practice Question

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

1. A.A and C
2. B.A and B
3. C.B and D
4. D.B and C