Question

The sum of two complex numbers $a+ib$ and $c+id$ is a real number if

• A. $a+c=0$
• B. $b+d=0$
• C. $a+b=0$
• D. $b+c=0$

Answer 1

The correct option is B $b+d=0$

It is given that

$z_1=a+ib$ and

$z_2=c+id$

Then
$z_1+z_2=(a+c)+i(b+d)$

Now
$(z_1+z_2)$ is purely real.

Then the imaginary part has to be $0$.

Hence
$b+d=0$.