(iv) * y + ix = 12 - 7i then x+y=

1 answer

To solve the equation \( (iv) y + ix = 12 - 7i \) for \( x + y \), we start by separating the real and imaginary parts.

The given equation can be rewritten as:

\[ y + ix = 12 - 7i \]

We compare the real part and the imaginary part from both sides:

  • The real part on the left side is \( y \).
  • The imaginary part on the left side is \( x \).

From the right side, we identify:

  • The real part is \( 12 \).
  • The imaginary part is \( -7 \).

This gives us the following system of equations:

  1. \( y = 12 \)
  2. \( x = -7 \)

Now, we can find \( x + y \):

\[ x + y = -7 + 12 = 5 \]

Thus, the solution is:

\[ \boxed{5} \]