How Do You Graph Complex Numbers?

Note:

To understand a complex number, it's important to understand where that number is located on the complex plane. This tutorial helps you practice graphing complex numbers!

Keywords:

problem
graph
graphing
complex numbers
complex plane
imaginary
real
z-plane

Background Tutorials

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
- What is the Coordinate Plane?
  
  You can't graph a function or plot ordered pairs without a coordinate plane! Learn about the coordinate plane by watching this tutorial.
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
- What is an Ordered Pair?
  
  Ordered pairs are a fundamental part of graphing. Ordered pairs make up functions on a graph, and very often, you need to plot ordered pairs in order to see what the graph of a function looks like. This tutorial will introduce you to ordered pairs!
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
- What's a Real Number?
  
  Real numbers are numbers that can be found on the number line. This includes both the rational and irrational numbers. This tutorial explains real numbers and gives some great examples. Take a look!