Transcript 2.1.7b multiply and divide complex numbers notes

2.1.7b Multiply/Divide Complex Numbers
Essential Question:
How do you multiply and divide complex numbers?
The Number System
Connecting Ideas
How do you multiply radicals and polynomials?
Multiplying complex numbers is similar to other
concepts. Let’s make connections to develop
mastery.
Multiply Polynomials
Review:
1) (4x)(5x)
2) 5x2(x + 3)
3) (x – 4)(x + 3)
Multiply Polynomials
• To multiply polynomials, we multiplied regular
numbers and put exponents of variables
together.
• We used Distributive Property and FOIL.
Radical Expressions
Review:
1) (4 3)(2
2)

2 4 6
2)

3) 3  8  7  6 
Multiply Radicals
• To multiply radicals, we multiplied regular
numbers and radicals.
• We simplified to reduce radicals.
• We used distributive property and FOIL.
Making Connections
• Using what you know about polynomials and
radical expressions, how do you think we will
multiply complex numbers?
• What should we watch out for?
• What kinds of values may need to be
simplified?
Multiply Complex Numbers
• How would you explain the process of
multiplying complex numbers to another
student?
• Write summarized steps in your notes.
Connecting Ideas
How do you divide radicals?
Dividing complex numbers is similar to other
concepts. Let’s make connections to develop
mastery.
Radical Expressions
Review:
1) 5
2
2)
3 3
2
3)
3 2
1 5
4)
4
6  10
Divide Radicals
• To divide radicals, you multiply numerator and
denominator by the value in the denominator.
• This is called rationalizing the denominator.
Meaning, we must have a rational number in
the denominator to be simplified.
• When the denominator is a binomial, we
multiply by the conjugate.
Conjugate
• Conjugates: opposite binomials in the form
a b
a b
Making Connections
• Using what you know about radical
expressions, how do you think we will divide
complex numbers?
• What should we watch out for?
• What kinds of values may need to be
simplified?
Dividing Complex Numbers
Practice
Divide Complex Numbers
• How would you explain the process of dividing
complex numbers to another student?
• Write summarized steps in your notes.
Summary
Answer the essential question in complete
sentences.
How do you multiply and divide complex numbers?
• STUDY QUESTIONS: Write 3-5 study questions in
the left column to help study and explain the
notes.