1. Multiplying and Dividing Complex Numbers
Honors Algebra II
Keeper 2

2. Multiplying:. Distribute & combine like-terms
Multiplying: *Distribute & combine like-terms* *Remember your rules of exponents*
Example: Simplify completely. 2𝑖(5 + 3𝑖) (3 + 2𝑖)(4 − 5𝑖) 3−2𝑖 2

3. You Try!!!
6𝑖 7−7𝑖 +𝑖(1+3𝑖)

4. You Try!!!
−2𝑖 −5−5𝑖 (2)(−7−6𝑖)

5. You Try!!!
5+ 8 𝑖 𝑖

6. Dividing:
Treat these just like you would dividing radical expressions. *No i's in the denominator* *Make sure i's are in simplest form* *THINK: What can I do to get 𝑖 2 or 𝑖 4 in the denominator?

7. Example: Simplify completely.
18 𝑖 12 6 𝑖 3 3 4𝑖

8. Special Cases:
When there is a complex number in the denominator, we must multiply by the complex conjugate in order to rationalize the denominator. Complex Conjugates − 𝟐 + 𝟑𝒊 → ____________ 𝟏 − 𝒊 →______________

9. Example: Simplify completely.
4+𝑖 5−2𝑖

10. Example: Simplify completely.
1+2𝑖 7+2𝑖

11. Example: Simplify completely.
3−3𝑖 −4𝑖

12. Example: Simplify completely.
9𝑖 3−𝑖

13. Example: Simplify completely.
5 −10𝑖

14. Example: Simplify completely.
5+ 6 𝑖 −1+ 3 𝑖