1. With a different method
Entry Task
With a different method

2. Target: I can identify and perform operations with complex numbers

3. -In the set of real numbers, negative numbers do not have square roots.
-Imaginary numbers were invented so that negative numbers would have square roots and certain equations would have solutions.
-These numbers were devised using an imaginary unit named i.
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4. it is a symbol for a specific number
Imaginary numbers:
i is not a variable
it is a symbol for a specific number

5. With your a/b partner determine the values for the cycle of i1 1 1 i i i -1 -1 -1 -i -i 1

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

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

8. Simplify the expression.

9. Simplify each expression.
Remember
Remember

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. -Express these numbers in terms of i.
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17. Conjugates
In order to simplify a fractional complex number, use a conjugate.
What is a conjugate?

18. are said to be conjugates of each other.

19. Lets do an example:
Rationalize using the conjugate
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20. Reduce the fraction

21. Lets do another example
Next

22. Try these problems.

24. Homework
Pg. 253 – #9,11,19,21,23,27,29,39,41,43,51,61

25. MULTIPLYING COMPLEX NUMBERS

26. ANSWERS
(-1)

27. (-1) =

28. Use the quadratic formula to solve the following:
a=3, b= -2, c=5 4 14

29. Let’s Review You need to be able to:
1) Recognize what i, i2, i3 ect. is equal to (slide 5)
2) Simplify Complex numbers
3) Combine like terms (add or subtract)
4) Multiply (FOIL) complex numbers
5) Divide (multiply by complex conjugates)