Find the real numbers x and y that make the equation true.
-$$( 7 + 2 i ) - 4 = x - ( - 7 + y i )$$
A) $x = - 4 , y = - 2$
B) $x = 4 , y = 2$
C) $x = 4 , y = - 2$
D) $x = 18 , y = - 2$

Question

Quizplus · Accepted Answer

Simplifying the given equation, we get $3 + 2i = x + 7 - yi$. Comparing real and imaginary parts, we find $x = 3 + 7 = 10$ and $y = -2$. However, there seems to be a mistake in my explanation as none of the provided options match the correct calculation. Correctly, simplifying the given equation should give $3 + 2i = x + 7 + yi$, leading to $x = 3 + 7 = 10$ and $y = 2$, but this also does not match any options directly, indicating a mistake in my initial calculation. Correctly, after re-evaluating, the equation simplifies to $3 + 2i = x + 7 + yi$, and comparing real and imaginary parts correctly should indeed give $x = 10$ and $y = 2$, but given the options and the mistake in my explanation, the correct approach is to directly compare both sides of the original equation after simplification: $(7 + 2i) - 4 = x - (-7 + yi)$ simplifies to $3 + 2i = x + 7 - yi$. Matching real and imaginary parts correctly, we should find that $x = 3 - 7 = -4$ and $y = -2$, which corresponds to option A. My apologies for the confusion in the explanation.

Find the Real Numbers X and Y That Make the Equation