Find the real numbers x and y that make the equation true.
-$$( - 4 - 2 i ) - 5 = x - ( - 7 + y i )$$
A) $x = - 16 , y = 2$
B) $x = - 6 , y = - 2$
C) $x = - 6 , y = 2$
D) $x = 8 , y = 2$

Question

Quizplus · Accepted Answer

First, simplify the left side of the equation: $(-4 - 2i) - 5 = -9 - 2i$. Then, simplify the right side to match the form $x + yi$, which gives $x + 7 - yi$. Equating real and imaginary parts, we get $x = -9$ and $y = 2$, but there's a mistake in my process since none of the options match this directly. Correctly simplifying the equation should give $x = -9 - 5 = -14$ and $y = -2$, but again, this doesn't match the options provided, indicating a mistake in my calculation. Correctly, we should directly compare the given equation to the options: $(-4 - 2i) - 5 = x - (-7 + yi)$ simplifies to $-9 - 2i = x + 7 - yi$. Correctly setting $x = -9 - 7 = -16$ and $y = 2$ matches option A, acknowledging my initial mistake in simplification.

Find the Real Numbers X and Y That Make the Equation