How Do You Add Complex Numbers by Graphing in the Complex Plane?

How Do You Add Complex Numbers by Graphing in the Complex Plane?

Note:

Did you know you can add two complex numbers together just by graphing them? This tutorial shows you how you can perform this addition on the complex plane!

Keywords:

  • problem
  • adding
  • add
  • complex numbers
  • graph
  • graphically

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 Origin?What is the Origin?

      What is the Origin?

      The coordinate plane has two axes: the horizontal and vertical axes. These two axes intersect one another at a point called the origin. Learn about the ordered pair that indicates the origin and its location in the coordinate plane by watching this tutorial!

      • What is the Coordinate Plane?What is the Coordinate Plane?

      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.

  • 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?What's a Real 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!

  • Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

      • How Do You Graph Complex Numbers?How Do You Graph Complex Numbers?

      How Do You Graph Complex Numbers?

      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!

  • Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

      • What is a Parallelogram?What is a Parallelogram?

      What is a Parallelogram?

      A parallelogram is a special type of quadrilateral with some special properties. In this tutorial, take a look at parallelograms and learn what kinds of quadrilaterals can also be called parallelograms!

Further Exploration

  • Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

      • How Do You Add Complex Numbers?How Do You Add Complex Numbers?

      How Do You Add Complex Numbers?

      If you want to add complex numbers together, first regroup them so that like terms are next to one another. Then, add the like terms together, and you have your answer! To see an example, check out this tutorial.