Imaginary Number: POWERS of i: Is there a pattern? Pattern repeats every 4th power: Divide power by 4 and use remainder Ex:

I ONE, I ONE! LOSERS IN THE MIDDLE LOSERS=NEGATIVE

Example 1: Simplifying Powers of i [B] [C] [D] [E] [E]

Example 2 Simplify Square Roots of Negative Numbers [C] [F] [D] [E]

Example 3 Multiplying Pure Imaginaries 1st: Convert all square roots into imaginary number notation [A] [B] [C] [D] [F] [E]

Example 4: Operations with Complex Numbers Complex Number: binomial term of real and imaginary # Add and Subtract: Combine Like Terms Multiply: FOIL, Distributive Property, Laws of Exponents Division: Rationalize with Conjugates [B] [A] [C] [D]

Example 5: Simplifying Using Complex Conjugates [B] [C] [D] Binomial Conjugate [E] Binomial Conjugate

Example 6: Equations with Imaginary Solutions Additional examples to come with quadratic formula [A] [B] [C] [D]

PRACTICE: Equations with Imaginary Solutions [B] [C] [D]