1. Complex Numbers

2. Definition of pure imaginary numbers: Any positive real number b, where i is the imaginary unit and bi is called the pure imaginary number.

3. Definition of pure imaginary numbers: i is not a variable it is a symbol for a specific number

4. Simplify each expression.

5. Remember Simplify each expression. Remember

7. Simplify. To figure out where we are in the cycle divide the exponent by 4 and look at the remainder.

8. Simplify. Divide the exponent by 4 and look at the remainder.

9. Simplify. Divide the exponent by 4 and look at the remainder.

10. Simplify. Divide the exponent by 4 and look at the remainder.

11. Definition of Complex Numbers Any number in form a+bi, where a and b are real numbers and i is imaginary unit.

12. Definition of Equal Complex Numbers Two complex numbers are equal if their real parts are equal and their imaginary parts are equal. If a + bi = c + di, then a = c and b = d

13. When adding or subtracting complex numbers, combine like terms.

14. Simplify.

16. Multiplying complex numbers. To multiply complex numbers, you use the same procedure as multiplying polynomials.

17. Simplify. F O I L

18. F O I L

19. The Habitat for humanity project utilizes volunteers to help build house for low – income families who might not be able to afford the purchase of a home. At a recent site, Habitat workers built a small storage shed attached to the house. The electrical blueprint for the shed called for two AC circuits connected in series with a total voltage of 220 volts. One of the circuits must have an impedance of 7-10j ohms, and the other needs to have an impedance of 9+5j ohms. According to the building codes, the impedance cannot exceed 20-5j ohms. Will the circuits, as designed, meet the code?