Modulus

Formal Definition

Define the modulus $|a+bi|$ of $a+bi$ by $|a+bi|=\sqrt{a^2+b^2}$.

Informal Definition

This absolute value is nonnegative real number and is the distance from $a+bi$ to the origin.

Example(s)

$|12+5i|=\sqrt{12^2+5^2}=13$.

Non-example(s)

$|12+5i|=\sqrt{12+5}=\sqrt{17}$.