Absolute Value of Complex Numbers

Complex numbers are in the form of a+bia+bi, Where ii is the Imaginary Unit, defined as the square root of minus 1.

Absolute Value is often viewed as the "distance" a number is away from 0, the origin. In the domain of Real Numbers, This is just the positive of that number, so the absolute value of -5 will be 5 and the absolute value of 5 will also be 5.

When it comes to the absolute value of Complex Numbers, we have to consider the Complex Plane. The Complex Plane is similar to the xy-Coordinate Plane, only instead of the x and y axis you have the real and imaginary axis. The Number 3+4i3+4i will have coordinates (3,4) on the complex plane.

How will we find the distance a number is from 0 on the complex plane? We can use the Pythagorean Theorem! The Absolute Value of a complex number is defined as:

a+bi=a2+b2|a+bi| = \sqrt{a^2 +b^2}

For Example, the Absolute Value of the complex number 3+4i3+4i is equal to:

3+4i=32+42=5|3+4i| = \sqrt{3^2 +4^2} = 5

Note by Yan Yau Cheng
5 years, 10 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

Also, note that the "absolute value" of a complex number is also called the "magnitude." I myself tend to use magnitude for non-real numbers, and absolute value for real numbers.

Michael Tang - 5 years, 10 months ago

Log in to reply

Problem: What is the absolute value of the product of two complex numbers? Use specific examples to aid in your findings. Can you generalize your statement in any way?

Bob Krueger - 5 years, 10 months ago

Log in to reply

@Yan Yau Cheng Can you add this to the Wiki page of Complex Numbers - Absolute Values? Thanks!

Calvin Lin Staff - 5 years ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...