- If there’s time, and if students can use the quadratic formula, there’s a nifty way to introduce complex numbers that’s in the spirit of their historical discovery, via CME.
- Have students create the arithmetic for complex numbers on their own
- Complex rotations put kids in contact with a cool and deep pattern while giving them bating practice with multiplication and division
- There is a nifty way to visually represent the complex solutions of quadratic equations.
- ???

Still looking for:

- A good problem set that helps students see that complex roots come in conjugate pairs

For all of the posts on complex numbers, click here.

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I wrote a poem about imaginary numbers. I’ve recently revised it to correct the history mentioned in the 3rd stanza. I just read a great chapter on that in

Journey Through Genius, by William Dunham.Here’s the history part:

…once upon a time (for real),

mathematicians dueled

by giving each other lists of thirty hard problems.

The winner got recognition

and perhaps a job.

All this dueling led to

a solution for cubic equations:

these mathematicians

created a formula

that would find the numbers

that would solve a thing

like 2×3-3×2+4x-5 = 0.

But that formula was a problem!

It came up with square roots of negative numbers,

which drove the mathematicians wild.

No, no, no. There is no such thing!

Well, maybe there could be…

and if there is,

what would it look like?

With a wave of the magic wand of imagination,

These mathematicians

made up a new number,

which later got the name i.

Of course the exponents came out wrong…