5.4 Complex Numbers

p. 272What 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?

Algebra 2C--Section 5.4•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:

x2 = 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).

Plotting Complex Numbersa)2 – 3i b) -3 + 2i c) 4i

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)

Complex Conjugates

The two factors of the last problem were6 + 3i and 6 – 3i. They have the form of a + bi and a – bi. They are like (a+b)(a−b)

that have a middle term of 0 when multiplied together.

The product of a complex conjugate is always a real number.

Dividing Complex Numbers

Write the quotient in standard form.

5 + 3i1− 2i

Finding Absolute Values of Complex Numbers

a) 3 + 4i1. Use the numbers in the

complex number 3 + 42. Square the numbers 32 + 42

3. Take the square root √32 + 42

Finding Absolute Values of Complex Numbers

b.-2i

c. -1 +5i

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 5.4

Page p. 277, 17-69 odd