Find the values of $x$x​ and $y$y​ that satisfy the equation.$2x-yi=14+12i$2x−yi=14+12i​$x=$x=​   and  $y=$y=​

1. Break Down the Problem

We need to solve the equation $2x - yi = 14 + 12i$. This involves separating the real and imaginary parts of the complex equation to find the values of $x$ and $y$.

2. Relevant Concepts

In any equation of the form $a + bi = c + di$, we can equate the real parts and the imaginary parts. Thus,

• Real part: $2x = 14$
• Imaginary part: $-y = 12$

3. Analysis and Detail

Step 1: Solve for $x$

From the real part of the equation: $2x = 14$ Dividing both sides by 2: $x = \frac{14}{2} = 7$

Step 2: Solve for $y$

From the imaginary part of the equation: $-y = 12$ Multiplying both sides by -1: $y = -12$

4. Verify and Summarize

Both values can be verified:

• For $x = 7$: $2(7) - (-12)i = 14 + 12i$
• This confirms both real part and imaginary part match with original equation.

Final Answer

The values are $x = 7$ and $y = -12$.