Transcript 1.6 Perform Operations with Complex Numbers

1.6 Perform Operations with
Complex Numbers
p. 41
What is an imaginary number?
How is it defined?
What is a complex number? How is it graphed?
How do you add, subtract, multiply and divide complex
numbers?
What is a complex conjugate? When do you use it?
How do you find the absolute value of a complex
number?
•She used her imagination to write the story.
•His imagination helped him with the role in
the play.
•He was able to draw the picture of the house
he wanted to build using his imagination.
•She had a tea party with her imaginary
friends.
•Define imagination.
•Define imaginary.
•What is the difference?
Solve:
2
x
=1
x2 = -1
Define the word:
complex
• He gave a complex explanation.
• It was a complex math problem.
• He turned a simple solution into a
complex solution.
Imaginary Unit Definition
i = √−1 and i 2 = −1
Complex number
A complex number is made up of a real
number and an imaginary number.
Standard form for a complex number is:
a + bi
a is the real part and bi is the imaginary part.
If a = 0 and b ≠ 0, then a + bi is a pure
imaginary number (0 + bi).
Adding and Subtracting Complex
Numbers
(4 – i) + (3 + 2i)
(7 – 5i) – (1 – 5i)
6 – (−2 + 9i) + (−8 + 4i)
Multiplying Complex Numbers
5i(−2 + i)
(7 – 4i)(−1 + 2i)
(6 + 3i)(6 – 3i)
Dividing Complex Numbers
Write the quotient in standard form.
5 + 3i
1− 2i
Finding Absolute Values of
Complex Numbers
a) 3 + 4i
1. Use the numbers in the
complex number 3 + 4
2
2
2. Square the numbers 3 + 4
3. Take the square root √32 + 42
Plotting Complex Numbers
a)2 – 3i
b) -3 + 2i c) 4i
Finding Absolute Values of
Complex Numbers
What is an imaginary number?
How is it defined?
What is a complex number? How is it graphed?
How do you add, subtract, multiply and divide
complex numbers?
What is a complex conjugate? When do you use
it?
How do you find the absolute value of a complex
number?
Assignment 1.6
p. 45, 3-47 odd
Skip 11,19,33,41
(last odd problem in each group)