1. Algebra 2 Warm up
11.12.13
Solve Each Equation
x
2
9 0
x 3 125 0
2 x 2 50 0

2. And now it’s time for..
The Lame Joke of the day..
What did the turkey say to the computer?
Google, Google, Google.

3. Definition
We know that
2 because (-2)(-2) =4
4
But how do you find
and (2)(2) =4
4 ?
It is not possible to multiply to numbers together that are the same
and get a negative number.
Therefore we need what is called imaginary numbers:
DEFINITION: i
Now we can simplify
1
AND
4
i2
4
1
1
4 i
2i

4. Compare
Real
9
25
11
50
Imaginary
3
9
3i
5
25
5i
11
11
i 11
25 2 5 2
50
25 2 5i 2
Summary: You take the square root as normal, but place an “i” to
get rid of the negative.

5. To simplify imaginary numbers
1. Imaginary numbers are like terms:
Ex: 5i + 3i = 8 i
2. Remember: i 2
1
3. Remove all negatives under square roots
before you do anything.
4. You can’t divide by an imaginary number.

6. Examples
16
4i 7i
3i
49
i 2 3i 2
4i 2
4
25
2i 5i
10i
2
10

7. More Examples
Most complicated:
i 2 i 3
i2 6
6
2
i
2 i
i i
2i
2
i
6
2
2i
6
i 2
6 i 2
i 2 i 2
6i 2 6i 2
2i 2
2
3i 2

8. Practice these on your own
• The solutions are on the next slide.
3
64
4
3i
9
3i 2
7
2i
2i 6i
i 7
4
2
8
4
18
9

9. Check your answers
• ANSWERS:
64
9
3i
3i 2
4
4
3i
7
7
7
2
2i
12
2
6i
4
i
3
3
2i 6i
i 7
3
8i
8
4
18
5i 2
9
6