1. U7D4 Have out: Bellwork: pencil, red pen, highlighter, GP notebook,
Identify the following for each equation, then graph the equations.
a) degree: ____
d) zeros: ________
b) leading coefficient: ____
e) y–intercept: ______
c) endpoint behavior: ____ 1) 2)
total:

2. c) endpoint behavior: ____1) +1 +1
a) degree: ____ 3
c) endpoint behavior: ____ +1
b) leading coefficient: ____
d) zeros: ________
3, –3, –3 +2
e) y–intercept: ______
(0, –3) +1
Double zero!!! +2

3. c) endpoint behavior: ____+1 2) +1
a) degree: ____ 4
c) endpoint behavior: ____ +1
b) leading coefficient: ____
d) zeros: __________
0, –5, 3, –2 +4
e) y–intercept: ______
(0, 0) +1 +2
total:

4. Complex Numbers Worksheet
two
Graph the function
However, there are ______ non–real zeros. Solve y x
Vertex (0, 1) –1 –1 –1
The square root of ____ is defined as ____, the ____________ unit. i
imaginary
There are ____ x–intercepts. no –1
Recall: x–intercepts are ______ zeros.
real

5. Exercise #1: Complete Exercise #2. 1) 2) 3) 4)
The rules of are true only for ________ numbers.
Before you multiply, you must _____________________________.
real
PULL YOUR “EYES” OUT!!!
Complete Exercise #2.

6. Exercise #2: 1) 2) 3) 4)

7. Exercise #2: 5) 6) 7) 8)

8. Exercise #2: 9)
10)
real
The product of imaginary numbers is __________.
(See problems #1, 3 – 5, 8 for a hint).

9. In this example, go right 3 from the origin. In this example, go up 2.
The Complex numbers are the _______ numbers combined with the _________ numbers, represented as _______.
real
imaginary
a + bi
imaginary
real
_________ part
_____ part
Complex numbers can be graphed on the _____________. The axes cross at _______, the origin of the complex plane.
complex plane
imaginary axis
(im)
0 + 0i 6i 4i
Example: Graph 3 + 2i
3 + 2i 2i
(re)
real axis
real part –6 –4 –2 2 4 6
complex part
Go left or right
–2i
Go up or down
In this example, go right 3 from the origin.
In this example, go up 2.
–4i
–6i

10. Plot each number on the complex plane
Plot each number on the complex plane. Categorize them as real, imaginary, or complex.
Exercise #3:
Be sure to accurately label the axes!!! im 2i 6i
Hint: 2i is the same as 0 + 2i. –4
Hint: –4 is the same as –4 + 0i. 4i
1+ 3i
1+ 3i 2i 2i
–3i –4 6 re –6 –4 –2 2 4 6 6
–2i
–3i
3 – 4i
–4i
3 – 4i
–6i

11. Plot each number on the complex plane
Plot each number on the complex plane. Categorize them as real, imaginary, or complex.
Exercise #3:
Real Numbers
Imaginary Numbers
Complex Numbers 2i –4 2i
1+ 3i –4
3 – 4i
1+ 3i 6
–3i –4
–4 + 0i
–3i 6
6 + 0i 6
Recall: The complex numbers are the real numbers combined with the imaginary numbers. Therefore ,any real or imaginary number can be written as a complex number.
0 + 0i
3 – 4i 2i
0 + 2i
–3i
0 – 3i

12. Exercise #4: Adding Complex Numbers:
Add ____ parts, and add __________ parts.
real
imaginary
Exercise #4:
Rewrite in a + bi form. 1) 2) 3) 4)

13. Exercise #5: Multiplying Complex Numbers:
Using a generic rectangle might help! 2
+ 3i
Example: 1 2
+ 3i
– 4i
– 8i
+ 12 2 3i
– 8i 12
= ___ + ___ + ___ + ___
= ___ + ___ 14
– 5i
Exercise #5:
Rewrite in a + bi form. 1) 2) 3) 4)

14. Exercise #5: Rewrite in a + bi form. 1) 2) –3 + 2i 5 – 3i 4 –12 + 8i 630
–18i
+ i
–3i –2
+ 2i
+10i +6

15. Exercise #5: Rewrite in a + bi form. 3) 4) 1 + i 4 – i 1 1 + i 4 16+1
– i
–4i –1 = = =

16. Finish today's Worksheets