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Absolute Value of a Complex Number

Master the concept of the absolute value of a complex number with interactive lessons and practice problems! Designed for students aged 10-16.

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Absolute Value of a Complex Number

Study Guide

Key Definition

The absolute value of a complex number $a + bi$ (also called the modulus) is defined as the distance between the origin $(0,0)$ and the point $(a,b)$ in the complex plane. It is represented as $|a + bi| = \sqrt{a^2 + b^2}$

Important Notes

The complex number is formed by real part 'a' and imaginary part 'b'.
The modulus is always a positive value or zero.
The absolute value or modulus is used in various fields like physics, engineering, and computer science.

Mathematical Notation

$a + bi$ represents a complex number where 'a' is the real part and 'b' is the imaginary part.

$|a + bi|$ represents the absolute value or modulus of a complex number.

In complex numbers, 'i' is the imaginary unit, which is the square root of -1.

Why It Works

The absolute value of a complex number is based on the Pythagorean theorem. It represents the distance from the origin to the point representing the complex number in the complex plane.

Remember

The absolute value of a complex number is always non-negative.

Quick Reference

Absolute Value Formula:$|a + bi| = \sqrt{a^2 + b^2}$

Understanding Absolute Value of a Complex Number

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The absolute value of a complex number is the distance from the origin to that number on the complex plane.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the absolute value of the complex number $-2 + 3i$?

Real-World Problem

Question Exercise

Intermediate

Electrical Engineering Scenario

In electrical engineering, complex numbers are used to analyze circuits. The absolute value represents the magnitude of the electrical quantity.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Suppose you have a complex number $4 - 7i$. What is its absolute value?

Challenge Quiz

Single Choice Quiz

Advanced

What is the absolute value of the complex number $5i$?

Recap

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Review key concepts and takeaways