Download Complex Numbers

Quick Crisp Review
• Simplifying Square Roots
• √24
√-72
Page 195
You will be able to simplify
complex numbers.
Complex number: written
in the form of a + bi where a
and b are real numbers and
i is the imaginary number.
1. 81
i  1
2.
121
2
i  1
3. 200x
Simplify each expression.
4. 8i  3i  24i  24 1
2
2
Remember i  1
 24
5. 5  20 i 5  i 20
Remember that
1  i
 i  100 110 10
2
Adding and Subtracting
Combine Like
Terms
Ex: 8  3i  2  5i 
8  2  3i  5i
10  2i
9 6i 12 2i 
9  6i 12  2i
 3 8i
Multiplying Complex Numbers
Similar to FOIL
8 5i2 3i
6 2i 5 3i 
Example 1
Write the quadratic equation in vertex
form.
f(x) = -x2 + 6x – 8
f(x) = -(x – 3)2 + 1
Example 2
Describe the right and left hand
behavior
y = 4x4 + 7x
Rises left and Rises Right
Example 3
Find the exact zeros of
x2 = 3x – 1
3 5
2
Example 4
Find the exact zeros of x2 = 2x – 5
1 2i
Example 5
Divide (2x3 + 9x2 + 14x + 5) ÷ (2x + 1)
x2 + 4x + 5
Example 6
Simplify
 6   24
2
3i 6
Exit
• What is a complex number and what are they
used for?
ACT: If x2 + 6x + 8 = 4 + 10x, then x equals
which of the following?
A) -2
B) -1
C) 0
D) 1
E) 2