Question

$Z_1,Z_2$ are two complex numbers such that $Z_1+Z_2$ is a complex number $Z_1{Z}_2$ is real number then

• A. $Z_2={\overline{Z}}_1$
• B. $Z_1=-{\overline{Z}}_2$
• C. $Z_1=Z_2$
• D. $Z_1{\overline{Z}}_2=1$

Answer 1

The correct option is B $Z_1=-{\overline{Z}}_2$

$z_1{z}_{2}isreal\Rightarrow z_2={\overline{z}}_{1}or{z}_2=-{\overline{z}}_1$
$[\because z_1\overline{z_1}=|z_1{|}^{2}and{z}_1(-\overline{z_1})=-|z_1{|}^2]$
but $z_1+z_2$ is a complex number
$\Rightarrow \overline{z_2}=-{\overline{z}}_1$