Transcript 2.1.7a complex numbers notes

2.1.7a Complex Numbers
Essential Questions:
What are complex numbers?
How can we simplify complex numbers?
Practice A - Discuss
Real Numbers
• The Real Number system contains all these
types of numbers.
• So when we said “All real numbers” as an
answer to an inequality or domain and range,
what did this mean about our values? Explain.
Imaginary Numbers
• Some numbers are not in the real number
system, but need to be represented when
dealing with mathematical concepts.
Imaginary Numbers
In the real number system, taking a square root
of a negative number was not possible within
that system. Therefore, we must use an
imaginary number.
Practice 1
Real + Imaginary = Complex
• Part of a number is real, but the other part is
imaginary, therefore, you write it as those
parts to make a complex number.
Practice 2
The Number System
Representing Complex Numbers
Practice 3
•
•
•
•
Graph
6 – 4i
-2 +5i
4i
Connecting Ideas
How do you add and subtract polynomials?
Adding and subtracting complex numbers is
similar to other concepts. Let’s make
connections to develop mastery.
Complex Numbers
• Just like polynomials and radical expressions,
we can add and subtract complex numbers.
How will we do that?
• Always simplify if possible. What kinds of
values may need to be simplified?
Practice 2
Radical Expressions
• Radical expressions involve rational numbers
and irrational numbers. Therefore, like
polynomials, we look for like terms. In this
case, like constants and like radicals.
• Always simplify radicals first: look for perfect
squares or cubes to take out of the radicand.
Simplifying First
• Practice
(4  9)  (6  16)
Summary
Answer the essential questions in complete
sentences.
What are complex numbers?
How can we simplify complex numbers?
• STUDY QUESTIONS: Write 3-5 study questions in
the left column to help study and explain the
notes.