1. 1.3 Complex Number System

2. Complex Numbers
Numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit.

3. Add / Subtract Complex Numbers
Change (– ) to (+) of the opposite
Apply the Distributive Property
Combine all like terms
Write your answer in the form of a + bi

4. Simplify each expression in standard form

5. Multiplying Complex Numbers
FOIL Method for multiplying binomials
Distributive Property for all other polynomials
Follow your rules of exponents
Combine all like terms
Write your answer in the form of a + bi

6. Simplify each expression in standard form

7. Conjugate

8. The conjugate of the conjugate of a complex number is the complex number itself.
The conjugate of the sum of two complex numbers equals the sum of their conjugates.
The conjugate of the product of two complex numbers equals the product of their conjugates.

9. Simplify using Conjugates

10. Dividing Complex Numbers
You cannot have an i in the denominator
Multiply numerator and denominator by the conjugate of the denominator
FOIL Method for multiplying binomials
Follow your rules of exponents
Combine all like terms
Write your answer in the form of a + bi

11. Simplify each expression in standard form

12. Evaluate Powers of i

13. Evaluate Square Roots
Perform the indicated operation and express your answer in standard form

14. Perform the indicated operation and express your answer in standard form

15. Character of Solutions

16. Determine the character of the solutions of each quadratic equation.

17. Solve each equation in the complex number system