The Argand Diagram sigma-complex It is very useful to have a graphical or pictorial representation of complex numbers. For example, the complex. are quantities which can be recognised by looking at an Argand diagram. number, z, can be represented by a point in the complex plane as shown in Figure 1. The easiest way to geometrically represent a complex number is by using an Argand Diagram (see above). The point Complex_files\Complex_MathML_jpg .

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Argand diagrams are, like graphs, a visual representation. Instead of representing an equation though, Argand diagrams represent numbers. Any number can be represented on an Argand diagram, be it real, imaginary or complex.

Argand Diagram

Mostly, though, it is used to show complex numbers. As you probably know, complex numbers are made up of a combination of real and imaginary numbers.


An Argand diagram has two axes, like a regular cartesian graph. However, in this case the horizontal axis represents real number, just like an ordinary number line you learnt about in primary school.

The vertical axis represents imaginary rumbers. The axes cross at zero, again just like in a cartesian graph.

Complex Plane

Then, extend a line from 0 to the point you just plotted. Some other properties are represented by the line on the Argand diagram.

The length of the line represents the modulus of the number: This angle, measured in radians, is known as the argument, and is important when representing complex numbers in polar form.

For many compleex of dealing with complex numbers, this form can be a lot more useful. So you can see, just from one line on an Argand diagram, you can learn a lot of the information you need to manipulate a complex number. Menu Log in Sign up. Answers Further Mathematics A Level. About the author Peter W.


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How do you plot a complex number in an Argand diagram? | MyTutor

Answered by Charlie M. How do I draw any graph my looking at its equation? Answered by Jasmin D. Get one-to-one help from a personally interviewed subject specialist.