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Exploring Patterns in Powers of i: Understanding Imaginary Numbers

Dive into the repeating patterns in powers of i every 4th power by dividing power by 4. Learn to simplify, multiply, and operate with complex numbers for a deeper understanding. Practice equations with imaginary solutions.

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Exploring Patterns in Powers of i: Understanding Imaginary Numbers

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

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

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

  4. [B] [C] [E] [D] [F] Example 2Simplify Square Roots of Negative Numbers [A]

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

  6. [C] 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] [D]

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

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

  9. [B] PRACTICE: Equations with Imaginary Solutions [A] [C] [D]

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