1. Complete Textbook p. 4 - #s1-6 p. 5 - #s 1-6
WARM-UP:
Simplifying Radicals
Complete Textbook p. 4 - #s1-6
p. 5 - #s 1-6

2. 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

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

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

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

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

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

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

10. You can't take the square root of a negative number, right?
When we were young and still in Coordinate Algebra, 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

11. 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?

12. Examples of how we use

13. Examples of how we use

15. Complex Numbers
Objective: You will write, add, subtract, multiply, and divide complex numbers.

16. a + bi: the standard form of complex numbers
- where a and b are real numbers
a = the real part of the complex number
bi = the imaginary part of the complex number
b = the coefficient of the imaginary number

17. Every real number is a complex number because a = a + 0i .
Complex Numbers
Real Numbers
Imaginary Numbers
Every real number is a complex number because a = a + 0i .
Every imaginary number is a complex number because bi = 0 + bi .

18. Imaginary Numbers
i = i1 = i i5 =
i2 = -1 i6 =
i3 = i7 =
i4 = i8 =