Question

The sum of two complex numbers $a+ib$ and $c+id$ is purely imaginary if

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

Answer 1

The correct option is A $a+c=0$

It is given that
$z_1=a+ib$ and
$z_2=c+id$
$z_1+z_2=(a+c)+i(b+d)$
$z_1+z_2$ is purely imaginary. (Given)
Then the real part has to be $0$.
Hence
$a+c=0$.