# What is the magnitude of numbers all about?

Mar 20, 2018

See below.

#### Explanation:

This is quite a big topic that I will try to explain simply but not completely here.

Put simply, "magnitude" of numbers refers to their size.

First, if we limit ourselves to the real numbers:

Then the magnitude of some $x \in \mathbb{R} = \left\mid x \right\mid$. That is the size of $x$ without concern as to whether it is negative or positive.

If we now extend to complex numbers:

Then the magnitude of some $z \in \mathbb{C} = a + i b$
where $\left\{a , b\right\} \in \mathbb{R}$ is $\sqrt{{a}^{2} + {b}^{2}}$ which is the absolute value of $z$ on the complex plane.

This concept can be extended further into other spaces, but in all cases the fundamental concept of magnitude is simply one of size - usually relative to other objects in the space.