When working with complex numbers, it’s important to understand their real and imaginary parts. Let’s break it down simply:

1. What is a Complex Number?
   A complex number looks like this: $a + bi$.
   Here, $a$ is the real part, and $b$ is the imaginary part.
   The letter $i$ represents the imaginary unit, which is the square root of $-1$.

2. How to Solve These Equations:
   When you solve complex equations, you can split them into two parts:

   • Real Part: This deals with the numbers that do not have $i$. You set the real parts equal to each other.
   • Imaginary Part: Here, you look at the numbers in front of $i$ and set those equal too.

3. Let’s Look at an Example:
   Take the equation: $(3 + 2i) + (x - 4i) = 7 + yi$.
   To find $x$ and $y$, we can separate it into real and imaginary parts:

   • For the Real Part: $3 + x = 7$
     This gives us $x = 4$.
   • For the Imaginary Part: $2 - 4 = y$
     So, $y = -2$.

By breaking down complex numbers like this, it becomes much easier to solve them.
It’s like solving two simple equations at the same time!