Absolute Value of Complex Numbers

Complex numbers are in the form of $a+bi$ , Where $i$ 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 $3+4i$ 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:

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

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

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

#ComplexNumbers #CosinesGroup

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Comments

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 - 7 years, 6 months ago

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 - 7 years, 6 months ago

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

Calvin Lin Staff - 6 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$