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 = 1 x x 2 = -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 + 2 i) (7 – 5 i) – (1 – 5 i) 6 – (− 2 + 9 i) + (− 8 + 4 i)
Multiplying Complex Numbers 5 i(− 2 + i) (7 – 4 i)(− 1 + 2 i) (6 + 3 i)(6 – 3 i)
Dividing Complex Numbers Write the quotient in standard form. 5 + 3 i 1− 2 i
Finding Absolute Values of Complex Numbers a) 3 + 4 i 1. Use the numbers in the complex number 3 + 4 2. Square the numbers 32 + 42 3. Take the square root √ 32 + 42
Plotting Complex Numbers a)2 – 3 i b) -3 + 2 i c) 4 i
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)
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