Answer
$\dfrac{8}{35} -i \dfrac{13}{28}$
Work Step by Step
We compute the total sum of complex numbers by combining the real and imaginary terms , then we add the functions by using the least common denominator (LCD) as follows:
$(\dfrac{-1}{5}+i \ \dfrac{2}{7} ) +(\dfrac{3}{7}-i \ \dfrac{3}{4} )=(\dfrac{-1}{5}+ \ \dfrac{3}{7} ) +\ i \ (\dfrac{2}{7}- \ \dfrac{3}{4} )$
or, $=(\dfrac{-7}{35}+ \dfrac{15}{35})+i(\dfrac{8}{28}- \dfrac{21}{28})$
or, $=\dfrac{8}{35} -i \dfrac{13}{28}$
