# 3. Graphical Representation of Complex Numbers

by M. Bourne

We can represent complex numbers in the **complex
plane.**

We use the **horizontal axis** for the **real**
**part** and the **vertical axis** for the **imaginary
part.**

### Example 1

The number `3 + 2j` (where `j=sqrt(-1)`) is represented by:

*j*

*A*

The point * A* is the representation of the complex number `3 + 2j.`

The horizontal axis is marked *R* (for the "real" numbered-component), and the vertical axis is marked *j* (for the imaginary component of the complex number).

## Adding Complex Numbers Graphically

### Need Graph Paper?

We can add complex numbers **graphically**.

This is the same idea as adding vectors graphically. See more at Adding 2D Vectors.

### Example 2

Add `1 + 2j` and `3 - j` graphically.

Answer

*j*

*j*

*j*

We add the complex numbers by setting up a parallelogram, just as we did when adding vectors. The solution is `(4 + j)`.

### Exercise

Perform graphically: `(3 - 2j) + (-1 - j)`

Answer

*j*

*j*

*j*

As we can see from the graph, the answer is `2 − 3j`.

See many more examples of adding vectors in an interactive applet over in the Vectors chapter.