Warm-up

• Solve for x. 1.

2.

3.

4. 0852

025

32954

64

2

2

2

2

xx

xx

x

x

Section 5-6: Complex Numbers

Goal 1.02: Define and compute with complex numbers.

Essential Questions

• What is an imaginary number?

• Why is it important to be able to compute with imaginary numbers?

Imaginary Numbers

1

1

1

4

3

2

i

ii

i

i

Simplifying Numbers using i:

Complex Number comprised of an imaginary and a real number of the form:

Complex Number Plane:

bia

i43

Absolute Value of a Complex Number:

a: |6 – 4i|

b: |-2 + 5i|

c: |5i|

22 babia

Additive Inverse of a Complex Number:

bia

i

i

i

3

34

52

Adding and Subtracting Complex Numbers:

ii

i

ii

ii

3)64(

)23(7

)42()38(

)62()75(

Multiplying Complex Numbers:

)34)(56(

)53)(32(

)32)(32(

)3)(7(

)4)(5(

ii

ii

ii

ii

ii

Dividing Complex Numbers:

iiiiii

iii

i

i

i

ii

i

5

1

5

8

5

8

41

624221

6342

21

21

21

3221

32

2

2

Multiply by the conjugate.

Multiply binomials.

Simplify.

Finding Complex Solutions:

a: 3x2 + 48 = 0

b: 4x2 + 100 = 0

c: 8x2 + 2 = 0

Classwork/ Homework

• P. 274• Classwork: #2-18 Even

• Homework: #20-46 Even