Question

Under what condition is the sum of two complex numbers $x_1+i{y}_1$ and $x_2+i{y}_2$ is purely real.

• A. $x_1+x_2=0$
• B. $y_1+y_2=0$
• C. $y_1+y_2=x_1+x_2$
• D. $x_1=y_1$,$x_2=y_2$

Answer 1

The correct option is B $y_1+y_2=0$

Let, $z=(x_1+i{y}_1)+(x_2+i{y}_2)$
$\Rightarrow z=(x_1+x_2)+i(y_1+y_2)$
Thus for $z$ to be purely real, $\text{Im}\left(z\right)=0$
$\Rightarrow y_1+y_2=0$