The Complex Number i

Algebra II-For Gifted Students

N.CN.1 Know there is a complex number such that = −1, and every complex number has the form with a and b real.

N.CN.2 Use the relation = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Objective Given the information provided and

previous knowledge of exponents, students will be able to compute the powers of i, and add and subtract complex numbers of the form 85% of the time. Each student will need a computer with

internet access, a pencil, and paper.

To begin…

(

Introducing an Imaginary Number Imagine a number where . Therefore .

So the

i

Patterns!

…

Activityhttps://www.khanacademy.org/math/trigonometry/imaginary_complex_precalc/i_precalc/e/imaginary_unit_powers

What is a Complex Number? A combination of real and imaginary

numbers. 𝑎+ 𝑏𝑖

Who can give an example of a complex number?

Adding and Subtracting Complex Numbers Addition

Ex.

Subtraction

Ex.

Solve…

Activityhttps://www.khanacademy.org/math/algebra/complex-numbers/complex_numbers/e/adding_and_subtracting_complex_numbers

QuizGrab a pencil and piece of paper and write down the questions and your answers.

1. Simplify:

2. Add/Subtract the following complex numbers: