When we want to understand how to work with complex numbers, it helps to visualize them on a graph. Here are some easy ways to do that:

1. Argand Diagram: This is the most common way to show complex numbers. We think of them as points in a flat space. On the graph, the real part of the number goes on the horizontal line (called the x-axis), and the imaginary part goes on the vertical line (the y-axis). For example, if we take the complex number $z = 3 + 4i$, we would plot it at the point (3, 4) on the graph.

2. Vector Addition: Adding complex numbers can be seen as adding arrows on the graph. If you have two complex numbers, $z_1 = a + bi$ and $z_2 = c + di$, you can find their sum $z_1 + z_2 = (a+c) + (b+d)i$. To do this, you place the start of $z_2$ at the end of $z_1$. The arrow that goes from the starting point to the end point shows the result.

3. Multiplication and Rotation: When we multiply complex numbers, it's like changing their length and turning them. For example, if we multiply by $i$ (which is like turning the arrow 90 degrees), the arrow rotates around the starting point. If we have a complex number $z = r(\cos \theta + i \sin \theta)$, multiplying by $i$ will change it to $r(\cos(\theta + 90^\circ) + i \sin(\theta + 90^\circ))$.

4. Magical Modulus and Argument: We can also use something called polar coordinates to show complex numbers. The modulus is how far the point is from the center, and the argument is the angle it makes with the positive x-axis. This way of looking at them can make it easier to see what happens when we multiply or divide complex numbers.

These techniques not only make it easier to understand complex number operations but also help us see their geometric shapes!