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` is represented by:

Represting 3+2j on the complex plane


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

Adding Complex Numbers Graphically

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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

Adding complex numbers graphically


We add the complex numbers by setting up a parallelogram. The solution is `(4 + j)`.

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Exercise

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

Answer

Adding complex numbers graphically

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.