Students meet the imaginary unit i — the square root of −1 — and the complex numbers it creates, expanding the number system so that even x² = −1 has a solution, and unlocking mathematics used across science and engineering.
Students will be able to…
“You can’t take the square root of a negative number.” But what if you could? Inventing one new number opens an entire new world of mathematics.
Project this and tap each idea. Have students learn how i works, how complex numbers are built, and why they matter.
Tap any phase to open the teacher moves and student actions.
√(−1) is “impossible” — so what if we just invented it?
Teacher models.
Class uses the Complex Explorer.
Students work with complex numbers.
One expression.
Aligned to the Common Core State Standards for Mathematics (High School: Algebra II).
Know there is a complex number i such that i² = −1, and every complex number has the form a + bi.
Add, subtract, and multiply complex numbers.
Solve quadratic equations with complex solutions.
Recognize when the quadratic formula gives complex solutions.
Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.
Have students multiply complex numbers (using i² = −1) and find the complex roots of a quadratic. A printable complex-numbers sheet is in the Math library.
Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.
A quick self-check with instant feedback, drawn from this lesson’s key terms.
A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.