What are Complex Numbers?

by Andrew Irving & Ebrahim Patel (on Tuesday 4th March 2014)

Despite their name, complex numbers aren’t that complicated.

The numbers we’re used to are called the real numbers (e.g. 5, 3/4, -2) and they use a building block of 1.

Real numbers such as 2 use 1 as their building block.
Real numbers such as 2 use 1 as their building block.

Real numbers are one-dimensional – this 1-D nature can be seen in the so-called number line.

Real number line with 2 marked on.
Real number line with 2 marked on.

However, there are lesser known numbers called the imaginary numbers (e.g. 2i, 4i/7, -9i) and they use a unique building block of i (the imaginary number).

Imaginary numbers such as 3i use i as their building block.
Imaginary numbers such as 3i use i as their building block.

Imaginary numbers are also one-dimensional – this 1-D nature can be seen in their own ‘number line’.

Imaginary number line with3ii marked on.
Imaginary number line with 3i marked on.

Complex numbers are nothing to be feared.  These are just numbers which use both building blocks (i and 1) at the same time.

Complex numbers such as 3i + 2 use 1 and i as their building blocks.
Complex numbers such as 3i + 2 use 1 and i as their building blocks.

Hence we use both number lines (the one for the real numbers and the one for the imaginary numbers) in tandem, producing a number plane.

Complex number plane with 3i + 2 marked on.
Complex number plane with 3i + 2 marked on.

So complex numbers are just two-dimensional numbers.

————————————————

Enjoy this blog?  Why not click “Like”!

Advertisements

1 thought on “What are Complex Numbers?

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s