What is the magnitude of numbers all about?

1 Answer
Mar 20, 2018

See below.


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 RR = absx#. 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 CC= a+ib#
where #{a,b} in RR# 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.