Find the real numbers x and y that make the equation true.
-$$( x + 6 i ) = ( 7 - i ) + ( 3 - 4 y i )$$
A) $x = 10 , y = 7$
B) $x = 4 , y = - \frac { 7 } { 4 }$
C) $x = 10 , y = - \frac { 7 } { 4 }$
D) $x = 10 , y = \frac { 7 } { 4 }$

Question

Quizplus · Accepted Answer

To solve for $x$ and $y$, we equate the real parts and the imaginary parts of the complex numbers on both sides of the equation. The equation given is $(x + 6i) = (7 - i) + (3 - 4yi)$.Equating the real parts gives us $x = 7 + 3$, which simplifies to $x = 10$.Equating the imaginary parts gives us $6 = -1 - 4y$, which simplifies to $7 = -4y$, and solving for $y$ gives $y = -\frac{7}{4}$.Therefore, the correct answer is $x = 10, y = -\frac{7}{4}$.

Find the Real Numbers X and Y That Make the Equation