Download 5-6 Complex Numbers

5-6 Complex Numbers
Algebra 2
Prentice Hall, 2007
Content Learning Objectives
You will…
• Learn what a complex number is.
• Write complex numbers in a+bi form.
• Simplify expressions containing complex
numbers.
• Graph complex numbers on a coordinate plane.
• Find the absolute value of a complex number.
What is it?
• The set of Complex Numbers consists of Real
and Imaginary Numbers
• The imaginary number, i, is equal to
1
What does it mean?
• Now, you CAN simplify radicals with negative
signs under the symbol! 
1  i
Ex. 1

36

Ex. 2

40

What does it mean?
• Complex numbers should be written in the
form
a  bi
Ex. 3
18  7



What else can you do?
• The imaginary number, i, ACTS like a variable
and all properties for +,-,x,/ apply!
Ex. 4 5  7i  2  6i
Ex. 5
6  4i  1 3i
Ex. 6
6  4i5  i


You can even graph it!
• The complex number plane is used to represent a
complex number geometrically.
• Graph the Real part on the
• Graph the Imaginary part
axis.
Ex. 7
3  4i
x-axis.
on the y-
What about Absolute Value?
• The absolute value of a complex number is its
distance from the origin on the complex
coordinate plane.
• Think Pythagorean Theorem…
a  bi  a  b
2
Ex. 7

3  4i
2
Assignment
• 5-6 p. 278: mo3 (3-66); +48 (for Bonus)
AND
p. 293: 18, 21, 45, 50