Mathematics - Complex Number Question with Solution | TestHub

For two non-zero complex number $z_1$ and $z_2$, if $Re\left(z_1{z}_2\right)=0$ and $Re\left(z_1+z_2\right)=0$, then which of the following are possible?

(A) $Im\left({\mathrm{z}}_1\right)>0$ and $Im\left({\mathrm{z}}_2\right)>0$
(B) $Im\left({\mathrm{z}}_1\right)<0$ and $Im\left({\mathrm{z}}_2\right)>0$
(C) $Im\left({\mathrm{z}}_1\right)>0$ and $Im\left({\mathrm{z}}_2\right)<0$
(D) $Im\left({\mathrm{z}}_1\right)<0$ and $Im\left({\mathrm{z}}_2\right)<0$

Choose the correct answer from the options given below: