Here is a puzzle that stumped grown-up mathematicians for hundreds of years:
Can you find a number that, times itself, gives negative one? 🤔
Don't worry if it seems impossible. By the end, you'll meet a special number called i that solves it!
Squaring a number means multiplying it by itself. We write a little 2 up high: 3² = 3 × 3 = 9.
It's called "squaring" because the dots make a square! Tap a number to build one.
Your turn: Which number, squared, makes 16?
Think of a number as an arrow on the number line. The arrow below points to 2.
Multiplying by −1 spins the arrow to face the opposite way!
Predict: If we do 2 × (−1), where will the arrow point?
If you turn around, then turn around again… you face forward again! 🧍➡️🔄🔄➡️
That's why a negative × negative gives a positive:
So 3² = 9 and (−3)² = 9. Any normal number squared is never negative.
Try it: What is (−2) × (−2)?
So no ordinary number squared can give −1… we need a brand-new kind of number! ✨
Times −1 is a half turn (facing the other way). What if we only turn halfway of that — a quarter turn, pointing straight up?
That's what multiplying by i does! The arrow leaves the number line and points to a new spot called i.
Mission: Tap × i to spin the arrow until it lands on the ⭐ glowing −1. Then press Check.
Two quarter turns make a half turn. So:
That's the mystery number from the start! We write it as i² = −1. Keep turning and the pattern goes round in a circle:
Match it: tap a power on the left, then its answer on the right. (Hint: count the quarter turns!)
The name imaginary is a bit of a joke — people once thought these numbers were silly. Now we use them everywhere! Tap each card to flip it.
Fun fact: the letter i stands for "imaginary". You'll learn more about it in secondary school and beyond! 🚀
You just solved a puzzle that puzzled mathematicians for centuries. 🎉