Complex Numbers

Videos and lessons to help High School students know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.

Suggested Learning Targets

• I know what are imaginary numbers and complex numbers.
• I can write complex number in the form a + bi with a and b real.
• I can simplify square roots of negative numbers using i.
• I can rewrite arbitrary powers of i.

Common Core: HSN-CN.A.1

Related Topics:
Common Core (The Complex Number System)

Common Core for Mathematics

Imaginary and Complex Numbers

Imaginary Numbers Introduction
i² = − 1
Solving Equations with i in the solution.

What Are Complex Numbers?
Imaginary Number: Square is a nonpositive real number
Complex Number: Square is a nonnegative real number
0 is both a complex and an imaginary number
Complex number has the form a + bi with a and b real
How to plot complex numbers on the Cartesian plane.

Introduction to i and Imaginary Numbers.

Square Root of Negative Numbers

Simplifying Square Roots of Negative Numbers Using i.



Expressing Square Roots of Negative Numbers with i
This video looks at simplifying square roots with negative numbers using the imaginary unit i. It includes 6 examples.

Rewrite Powers of i

Calculating i Raised to Arbitrary Exponents.



Rewriting Powers of ' i ' - Ex 1
Complex number ' i ', raise it to some different powers, and simplify.

Rewriting Powers of ' i ' - Ex 2
i raise to a negative power.