1. 5.4 Complex Numbers Until now, you have always been told that you can’t take the square root of a negative number. If you use imaginary units, you can! OBJ: To solve quadratic equations with complex solutions & perform operations with complex numbers

2. Imaginary Unit The imaginary unit is ¡ ¡= It is used to write the square root of a negative number

3. Property of the square root of negative #s If r is a positive real number, then: Ex 1:

4. *For larger exponents, divide the exponent by 4, then use the remainder as your exponent instead. Ex 2:

5. Ex 3: a.b.

6. Complex Numbers A complex number has a real part & an imaginary part. Real part Imaginary part Like: 5+4i

7. Adding and Subtracting (add or subtract the ”matching” parts) Ex 4: Ex 5: Ex: 6

8. Homework

9. Multiplying (Treat the i’s like variables, then simplify any that are not to the first power) Ex 7: Ex 8:

10. Ex 9:

11. Dividing (Multiply the numerator and the denominator by the “conjugate”) Ex 10:

12. Absolute Value of a Complex # If you have a complex number the absolute value can be found using:

13. Ex 11 : a. b.