Yeah. DJ Stablefree on the track.
This %#@! we're exploring. It's gonna be magical.
I got a cold, so if I'm nasal, then $#&@ you.

I'll tell you a maths joke if you make fun of my accent, bro!

Don't $#&@ with mathematicians!

We can use maths to kill you with dubstep!
Or create a car. With magnets.


Yeah, so whatcha know about complex numbers, son?

W-elcome fellow bronies

Your teacher Stablefree
If you thought numbers were bad,
Then this is something to see.


When using only real numbers
We have some dificulties

You can't evaluate roots
With negativity.


But if you introduce 'i'
The complex identity,
then solving 'root of neg 1'

Is an easy feat.

Square root of negative 'n'

Is just root 'n' times 'i'
That's the basics of complex
numbers, easy as π!


When factorising poly-
nomials in the complex field

then 'neg b plus minus root b squared minus
4 a c over 2 a' is of massive appeal!


Hey. don't doze off just yet.
We've got some trig to cover.


And now some co-ordinate
Geometry
An Argand Diagram is similar

To that of a Cartesian plane

A complex number z

Is x + iy,
Then you go x to the left,
Then go up by y, it's easy!


Then draw a line
origin to the point.

It's length is modulus z,
Inclined by argument z.


Put this into trig form,
cos plus i sin of arg
negative arg is conjugate z

It's not that hard!

De Moivre's (spoken anglicised i.e. wrongly) Theorem states that

cis theta to the power of n
is equal to cis of theta times n, which is
Used-in trigono-metric identities!


Yeah. Complex numbers.
You'd better be taking notes.

I'm giving you a test after this.
It's gonna be $#&@ing tough.
Next time, I'mma teach you

about vectors. And locii.
And complex roots of unity.
Cool %#@! like that. Get pumped.


Okay. Time for lunch.
I-Pie, you stay here.

You got a B plus in your last test.
You know what happens when you get a B plus.
I whip a (*##$. Hard.
And tell you lame maths jokes.
Yeah, be scared.

Stablefree, out.