1. Complex and Imaginary Numbers

2. In the beginning… There was ONE. ONE was a concept, but not formally a number. The earliest evidence of the number 1 is 20,000 years old and is in the form of notches on a bone. Deseret News, http://www.deseretnews.com/article/865560110/A- brief-history-of-numbers-and-counting-Part-1-Mathematics-advanced- with-civilization.html?pg=all

3. Leap 25,000 Years When the Indians invented ZERO. This was a huge leap in math. It allowed for calculations that could never before be done. ……. Then there were fractions There was a need identified for people to think in terms of parts of things, and not just whole things.

4. But what other numbers were there? If we can multiply 2 by itself and get 4, is there a number we can multiply by itself to get 5? Is it possible to have a square whose area is 3? If so, how long would the sides be? Solving problems like these led to the discovery a new set of numbers – the irrational numbers.

5. The square root of -1?

6. Complex numbers contain real numbers ( a and b) and an imaginary number i

7. The square root of a negative number has no real solution, but it does have an imaginary one: Imaginary Unit i

11. Do Now: Simplify the expression by rationalizing the denominator Example: a. b.

12. Why Do We Rationalize the Denominator?

15. Index Card Activity Create your own complex number division expression and write it on the front of the index card Simplify it and write the answer on the back of the card Switch cards with a partner and try to solve it!