A number with two components.
Written as a+bi
where a is the
part and b is the imaginary part.
Recall that real numbers are those that lie on a
number line. Complex numbers extend this idea to numbers that lie on a two dimensional flat plane.
Complex numbers have two components called the real and imaginary parts written like this:
where i is the square root of -1.
They can be plotted on a 2-dimensional plane
If we plot the real part along the horizontal x axis, and the imaginary part along the vertical y axis, each complex number occupies one unique spot on the plane. In the figure below, as you drag the orange point around, you can see what complex number corresponds to that location.
What are they used for?
They are used in many engineering disciplines, for example for solving equations that describe complex electrical circuits.
Because the letter i is used to mean current in electrical engineering, it is often replaced with the letter j instead.
Related number topics
(C) 2009 Copyright Math Open Reference. All rights reserved
Math Open Reference now has a Common Core alignment.
See which resources are available on this site for each element of the Common Core standards.
Check it out