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

4. Simplify each expression.

5. Simplify each expression.
Remember
Remember

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

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

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

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

11. Simplify.

12. Simplify.

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

14. Simplify. F O I L

15. Simplify. F O I L

16. Conjugates
In order to simplify a fractional complex number, use a conjugate.
What is a conjugate?

17. are said to be conjugates of each other.

18. Lets do an example:
Rationalize using the conjugate
Next

19. Reduce the fraction

20. Lets do another example
Next

21. Try these problems.