Let's solve problems 14, 15, and 18 from the image. These involve solving for $x$ and $y$ in equations with real and imaginary parts.

Problem 14:

$3x + 6i = 27 + yi$

1. Separate real and imaginary parts:

   • Real part: $3x = 27$
   • Imaginary part: $6i = yi$

2. Solve each equation:

   • For the real part: $3x = 27$ → $x = 9$
   • For the imaginary part: $6 = y$

Thus, $x = 9$ and $y = 6$.

Problem 15:

$-10x + 12i = 20 + 3yi$

1. Separate real and imaginary parts:

   • Real part: $-10x = 20$
   • Imaginary part: $12i = 3yi$

2. Solve each equation:

   • For the real part: $-10x = 20$ → $x = -2$
   • For the imaginary part: $12 = 3y$ → $y = 4$

Thus, $x = -2$ and $y = 4$.

Problem 18:

$-12x + yi = 60 - 13i$

1. Separate real and imaginary parts:

   • Real part: $-12x = 60$
   • Imaginary part: $yi = -13i$

2. Solve each equation:

   • For the real part: $-12x = 60$ → $x = -5$
   • For the imaginary part: $y = -13$

Thus, $x = -5$ and $y = -13$.

Would you like further details on any of these solutions, or do you have any questions?

Here are 5 related questions:

1. How do we separate real and imaginary parts in complex equations?
2. What if the equation had more complex coefficients, how would we approach it?
3. How would you verify the solution to a complex number equation?
4. How can we apply these concepts to systems of complex equations?
5. Why is it important to equate real and imaginary parts separately?

Tip: Always make sure the imaginary unit $i$ is factored correctly when isolating terms in complex number equations.