1. Warm-up
Simplify as far as possible, do not make a decimal. Your answer will still have a square root sign in it.
1. (5 + 4x) + (7 - 2x)

2. How do we take the square root of negative numbers?
Math II Day 2 (1-5-11)
Standard MM2N1
a - Write square roots of negative numbers in imaginary form.
b - Write complex numbers in the form a+bi.
Today’s Question:
How do we take the square root of negative numbers?
Standard: MM2N1.a, b, c, d

3. in a math class far, far away..
A long long time ago,
in a math class far, far away..
There was no way
to take the square root
of a negative number

4. Every time we squared a negative number
We got a positive.

5. (-1) = 1
(-2) = 4
(-3) = 9

6. that when multiplied by itself
Was there a number,
that when multiplied by itself
Gave you a negative???

7. Can we in fact, take the square root
of a negative number?
WE CAN!!!!

8. Ladies and Gentlemen of Math II
I present to you
a NEW number...
A number so complex...

9. It stretches the imagination..
I present to you:

11. You can't take the square root of a negative number, right?
When we were young and still in Math I, no numbers that, when multiplied by themselves, gave us a negative answer. 
Squaring a negative number always gives you a positive.   (-1)² = 1. (-2)² = 4 (-3)² = 9

12. So here’s what the math people did: They used the letter “i” to represent the square root of (-1). “i” stands for “imaginary”
So, does
really exist?

13. Examples of how we use

14. Examples of how we use

16. ?

17. 1.3 Powers of i and Multiplying Complex Numbers

18. *For larger exponents, divide the exponent by 4, then use the remainder as your exponent instead.
Example:

20. $25,000 Pyramid

21. $25,000 Pyramid i -i 1 i -1 -i -1 -i 1 -1

22. Multiplying Treat the i’s like variables, then change any that are not to the first power
Ex:
Ex:

23. Remember the area method
(6x+2)(4x-5)
24x2 + 8x -30x -10
=24x2 – 22x -10 4x -5 6x
24x2
-30x 2 8x
-10

24. Your Turn!

25. Your Turn!

26. Assignment
Page 4 –
Page 8 –
Page 14 –

27. Complex Numbers A complex number has a real part & an imaginary part.
Standard form is:
Real part
Imaginary part
Example: 5+4i

28. The Complex Plane
Real Axis
Imaginary Axis

29. Graphing in the complex plane

30. Absolute Value of a Complex Number
The distance the complex number is from the origin on the complex plane.
If you have a complex number
the absolute value can be found using:

31. Graphing in the complex plane5 2

32. Examples 1. 2.
Which of these 2 complex numbers is closest to the origin?
-2+5i

33. Try These!!! 1. 2.
Which of these 2 complex numbers is closest to the origin? 3i