CP Algebra II 11/12/15
Complex Numbers
1.
Name: __________________ 4-4 Intro to
Graph: f (x) = x 2 + 4x - 12
y-intercept:
A.O.S.:
Vertex:
Domain:
Range:
2.
Graph: f (x)  x 2  5
y-intercept:
A.O.S.:
Vertex:
Domain:
Range:
3.
x-intercept(s):
x-intercept(s):
What are the solutions to the function f (x)  x 2  5 , and how does the graph represent those
solutions?
4.
Support your conclusion from questions 2 and 3 by solving f (x)  x 2  5 algebraically to find the xintercepts.
There are solutions to f (x)  x 2  5 that are not in the set of real numbers. Mathematicians developed
imaginary numbers to solve such equations.
Definition: Imaginary Unit: i  1
Definition: Complex Number: z  a  bi
5.
Identify the real and imaginary parts given each complex number.
a.
z  3i  4
b.
z=4
6.
2 3 4
5
Calculate the values of i ,i ,i , and i .
7.
Evaluate.
a.
8
i 14
b.
c.
i 78
z  8i  13
d.
c.
Perform the indicated operation for the complex numbers:
a.
(10  2i)  (4  8i)
b.
(10  2i)  (3  7i)
i 308
z = -3i
c.
9.
(3  2i)(4  3i)
d.
3i
2  3i
Solve.
a.
x 2  16
b.
3x 2  12  0
Assignment:
1.
Simplify:
a.
d.
121
i 13
b.
i6
c.
e.
(2  3i)  (4  5i)
f.
72
2i(3  7i)
2.
g.
5  2i
3  2i
h.
j.
5i  12  i  13
k.
(2  7i)(3  4i)
i.
3i
7  2i
l.
Solve.
a.
x 2 + 121 = 0
b.
- 5x 2 - 50 = 0
96
(8  3i)(2  i)