The decimal numbers we play with in grade school are called the real numbers and can be modeled as points on a single line we call the real number line. On the other hand, complex numbers are two-dimensional and are modeled as points on a 2D surface like a computer screen. Traditionally we talk about the left-to-right placement of the number as the real component and the bottom-to-top placement as the imaginary component. To add two complex numbers we just add their real components together and then their imaginary components together.
Drag the green and blue points and watch how they sum to the red point. The "choose" radio buttons let you pretend you're sliding the green vector (arrow) from the origin to the tip of the blue vector or the other way around. Either way, you end up at the red point: red = green + blue, or red = blue + green. Mathematicians call this phenomenon commutativity.