For two non-zero complex number $z _ { 1 }$ 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) $\operatorname { Im } \left( \mathrm { z } _ { 1 } \right) > 0$ and $\operatorname { Im } \left( \mathrm { z } _ { 2 } \right) > 0$ (B) $\operatorname { Im } \left( \mathrm { z } _ { 1 } \right) < 0$ and $\operatorname { Im } \left( \mathrm { z } _ { 2 } \right) > 0$ (C) $\operatorname { Im } \left( \mathrm { z } _ { 1 } \right) > 0$ and $\operatorname { Im } \left( \mathrm { z } _ { 2 } \right) < 0$ (D) $\operatorname { Im } \left( \mathrm { z } _ { 1 } \right) < 0$ and $\operatorname { Im } \left( \mathrm { z } _ { 2 } \right) < 0$ Choose the correct answer from the options given below: (1) B and D (2) B and C (3) A and B (4) A and C
For two non-zero complex number $z _ { 1 }$ 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) $\operatorname { Im } \left( \mathrm { z } _ { 1 } \right) > 0$ and $\operatorname { Im } \left( \mathrm { z } _ { 2 } \right) > 0$\\
(B) $\operatorname { Im } \left( \mathrm { z } _ { 1 } \right) < 0$ and $\operatorname { Im } \left( \mathrm { z } _ { 2 } \right) > 0$\\
(C) $\operatorname { Im } \left( \mathrm { z } _ { 1 } \right) > 0$ and $\operatorname { Im } \left( \mathrm { z } _ { 2 } \right) < 0$\\
(D) $\operatorname { Im } \left( \mathrm { z } _ { 1 } \right) < 0$ and $\operatorname { Im } \left( \mathrm { z } _ { 2 } \right) < 0$\\
Choose the correct answer from the options given below:\\
(1) B and D\\
(2) B and C\\
(3) A and B\\
(4) A and C