1. Imaginary Numbers ???

2. In real life, complex numbers are used by engineers and physicists to measure electrical currents, to analyze stresses in structures such as bridges and buildings, and to study the flow of liquids.

3. Engineers who design speakers use complex numbers. Engineers who design and test the strength of bridges use complex numbers. Scientists who do experiments on ways to make energy using fuel cells, batteries, and solar cells use complex numbers.

4. Complex numbers are also used for generating fractals, which are geometric objects created by making a repeating pattern.

9. Which is actually very useful because… …by simply accepting that i exists lets us solve things where we need the square root of a negative number.

10. Example: What is the square root of -25? Answer:

13. A few questions… Simplify Simplify A) B) A) B)

18. Question 1

19. Question 2

20. Question 3

21. Question 4

22. Complex Numbers

24. Complicated?

26. Try it! +

30. Solve Graph it! Can you solve it graphically? What do you notice?

31. Solve Algebraically!

34. Practice! Simplify. Practice! Simplify. a) b) c) d) e) f)

35. Solve: