1. Complex Numbers 22 11 Simplifying Addition & Subtraction 33 Multiplication

2. Remember: Imaginary Number (i)  Defined as:  Powers of i 2

3. Simplifying Monomials  Simplify a Power of i  Steps  Separate i into a power of 2 or 4 taken to another power  Use power of i rules to simplify i into -1 or 1  Take -1 or 1 to the power indicated  Recombine any leftover parts 3

4. Operations  Simplify a Power of i Simplify 4

5. Simplifying Monomials Example  Square Roots of Negative Numbers Simplify 5

6. Addition & Subtraction  Add and Subtract Complex Numbers  Treat i like a variable Simplify 6

7. Ex: Addition & Subtraction Examples

8. Multiplying Complex Numbers  Multiply Pure Imaginary Numbers  Steps  Multiply real parts  Multiply imaginary parts  Use rules of i to simplify imaginary parts 8

9. Monomial Multiplication Example  Multiply Pure Imaginary Numbers Simplify 9

10. Multiplication Example  Multiply Complex Numbers Simplify 10

11. Solving ax 2 +b=0  Equation With Imaginary Solutions Solve Note: ± is placed in the answer because both 4 and -4 squared equal 16 11