Complex Numbers

When it comes to complex numbers,

You may notice a strange guy,

Who and Why?

That guy is the imaginary number i.

Look at how i divides a pie

Into 4 pieces, as i, -1, -i, 1,

And i is i,

i squared is negative one, -1,

i cubed is opposite of i, -i,

i fourth is positive one, 1.

If you want to go further with the power of i,

You know i fifth is the same as i,

Because 5 is 4+1,

And i fourth power goes back to 1.

Thus the power of i is easy to simplify.

To learn more,

Divide any power of i by four, 4.

Complex solutions always come in pairs,

a+bi, a-bi are conjugate pairs.

Addition, Subtraction,

Multiplication, and Division,

All work the same wonders

In complex numbers

As they do in real numbers.

Make sure real parts go with real parts,

Imaginary parts join imaginary parts.

The final expression will always be a+bi,

With a, b either a whole number or a fraction.

If b is a fraction,

Make sure i sits on top,

Otherwise,

Make 1 over i equal to negative i, -i.

Do you understand the function of i?

I like i,

Please don’t ask me why!