Final answer:
By comparing the real and imaginary parts of the complex numbers, we can find x=9 and y=-3. However, this result does not match any of the given answer choices, indicating a potential error in the options provided.
Step-by-step explanation:
The student has asked to find the values of $x$ and $y$ that satisfy the complex number equation $ 36-yi = 4x + 3i$. To solve this, we should equate the real parts and the imaginary parts of the complex numbers on both sides of the equation separately.
The real part is 36 on the left side and 4x on the right side, giving us $x = 9$ once we divide both sides by 4. Similarly, by equating the imaginary parts, -y on the left side and 3 on the right side, we can deduce that $y = -3$. However, there seems to be a typo in the options, as none of them contain the value $y = -3$. Therefore, none of the given choices are correct.
To solve the equation $36-yi=4x 3i$, we need to match the real parts (36-y) and the imaginary parts (3yi).
Matching the real parts, we have: $36 = 4x$, which gives us $x = 9$.
Matching the imaginary parts, we have: $-y = 3$, which gives us $y = -3$.
So the values of $x$ and $y$ that satisfy the equation are $x = 9$ and $y = -3$.