Question

select the correct answer.

what are the the values of \\(x\\) and \\(y\\) that satisfy this equation?
\\(x + yi) + (4 + 9i) = 9 - 4i\\

\\(x = 5\\) and \\(y = 13\\)
\\(x = 5\\) and \\(y = -13\\)
\\(x = 9\\) and \\(y = -4\\)
\\(x = -9\\) and \\(y = 4\\)

Explanation:

Group the real and imaginary parts

$$ (x + 4) + (y + 9)i = 9 - 4i $$

Set up equations for real and imaginary components

$$
LATEXBLOCK0
$$

Solve for x and y

$$
LATEXBLOCK1
$$

Answer:

• (A) \(x = 5\) and \(y = 13\)
• (B) \(x = 5\) and \(y = -13\) (Correct answer)
• (C) \(x = 9\) and \(y = -4\)
• (D) \(x = -9\) and \(y = 4\)