How Do You Find the Absolute Value of a Complex Number?

Note:

The absolute value of a complex number is just the distance from the origin to that number in the complex plane! This tutorial shows you how to use a formula to find the absolute value of a complex number.

Keywords:

problem
absolute value
complex numbers
pythagorean theorem
complex plane
distance from zero

Background Tutorials

Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.
- What's a Prime Number?
  
  Prime numbers aren't too hard to define, but they still puzzle professional mathematicians. Believe it or not, all over the word computers are chugging away, trying to find the next biggest prime! Bigger and bigger prime numbers help keep your credit card info safe through really cool encryption techniques. So prime numbers really matter every day, and you can learn how they are defined in this tutorial.
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?
  
  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?
  
  You can't graph a function or plot ordered pairs without a coordinate plane! Learn about the coordinate plane by watching this tutorial.
Write and evaluate numerical expressions involving whole-number exponents.
- How Do You Square a Number?
  
  Want to square a number? Just take the number and multiply it by itself! If you square an integer, you get a perfect square! Check out squaring in this tutorial!
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
- What is the Substitution Property of Equality?
  
  If you ever plug a value in for a variable into an expression or equation, you're using the Substitution Property of Equality. This property allows you to substitute quantities for each other into an expression as long as those quantities are equal. Watch this tutorial to learn about this useful property!
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!
Explain a proof of the Pythagorean Theorem and its converse.
- What is the Pythagorean Theorem?
  
  The Pythagorean theorem is a very popular theorem that shows a special relationship between the sides of a right triangle. In this tutorial, you'll get introduced to the Pythagorean theorem and see how it's used to solve for a missing length on a right triangle!