Question

find the desired sum or difference.

\\((5 - 4i) - (-5 + 7i)\\)

\\((5 - 4i) - (-5 + 7i) = \square\\)
(simplify your answer. type your answer in the form \\(a + bi\\).)

Explanation:

Distribute the negative sign

Using the Complex Numbers knowledge point

$$ -( -5 + 7i ) = 5 - 7i $$

Group real and imaginary parts

Using the Complex Numbers knowledge point

$$ (5 - 4i) - (-5 + 7i) = 5 - 4i + 5 - 7i = (5 + 5) + (-4i - 7i) $$

Combine like terms

Using the Complex Numbers knowledge point

$$ (5 + 5) + (-4 - 7)i = 10 - 11i $$

Answer:

\( (5 - 4i) - (-5 + 7i) = \) <blank>\(10 - 11i\)</blank>