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Site Menu: Introduction Argand Diagrams Complex Algebra De Moivre's Theorem Complex Conjugates Links: Learn Html At www.w3schools.com/html More On Complex Numbers At www.ping.be And At http://scholar.hw.ac.uk Interesting Problems On Complex Numbers At www.nrich.maths.org |
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-Argand Diagrams-
The complex plane is called an argand diagram. It is used to plot a complex number. On the horizontal axis are the real numbers and on the vertical axis are the imaginary numbers. Here is an example of an argand diagram:
As in polar co-ordinates, a complex number can be defined by its distance from the origin (modulus) and angle (in radians) from the positive real axis (argument). It can be written as (r,θ), wher r is the modulus and θ is the argument. A complex number, x+i.y, is the same as r(cos(θ) + sin(θ)). Then there is an identity r(cos(θ) + sin(θ)) = reiθ, which can be checked by differentiating both sides. From this comes a very interesting result; eiπ = -1.
Some interesting results and transformations on argand diagrams can be found at www.waldomaths.com. Click on the link and from the left hand menu go to 16-19, further mathematics, complex numbers.