• How do I graph and find the absolute values of complex numbers?

1.4 Use the Complex Plane

Example 1 Plot the complex numbersPlot the complex numbersPlot the complex numbers in the same complex plane.

i42 a. i31 b. i44 c. i3 d. i22 e.

i

1 real

imaginarya. To plot 2 + 4i, start at the origin, move 2 units _____, then move 4 units ___.

rightup

b. To plot 1 3i, start at the origin, move 1 unit _____, then move 3 units ______.

rightdown

c. To plot 4 4i, start at the origin, move 4 units _____, then move 4 units ____.

leftup

d. To plot 3i, start at the origin, move 3 units ______.down

e. To plot 2 2i, start at the origin, move 2 units _____, then move 2 units ______.left down

1.4 Use the Complex PlaneCheckpoint. Complete the following exercise. Checkpoint. Complete the following exercise.

Plot the complex numbers in the same plane.

i34 1. i23 2. i5 3.

i

1 real

imaginary

1.4 Use the Complex Plane

Example 2 Find the absolute values of complex numbersFind the absolute values of complex numbersFind the absolute value of the complex number.

i23 a. i35 b. i63 c. i4 d.Solution

i23 a.

22 _______ Definition of _______________. valueabsolute3 2______ Evaluate powers.9 4

_____ Simplify.13

1.4 Use the Complex Plane

Example 2 Find the absolute values of complex numbersFind the absolute values of complex numbersFind the absolute value of the complex number.

i23 a. i35 b. i63 c. i4 d.Solution

i35 b.

22 ______ Definition of absolute value.5 3

______ Evaluate powers.25 9

_____ Simplify.34

Evaluate ______________.

1.4 Use the Complex Plane

Example 2 Find the absolute values of complex numbersFind the absolute values of complex numbersFind the absolute value of the complex number.

i23 a. i35 b. i63 c. i4 d.Solution

i63 c.

22 _______ Definition of absolute value.

root square

3 6______ Evaluate powers.9 36

___ Simplify.45_____ 53

Evaluate square root.

1.4 Use the Complex Plane

Example 2 Find the absolute values of complex numbersFind the absolute values of complex numbersFind the absolute value of the complex number.

i23 a. i35 b. i63 c. i4 d.Solution

i4 d.22 ______ Definition of absolute value.0 4

______ Evaluate powers.0 16

___ Simplify.16___ 4

1.4 Use the Complex PlaneCheckpoint. Find the absolute value of the complex Checkpoint. Find the absolute value of the complex number.number.

i35 4.

25

23

25 9

34

i84 5.

24

28

16 64

80

80

8 10

2 4 5 2

2 252222 22

54

1.4 Use the Complex PlaneCheckpoint. Find the absolute value of the complex Checkpoint. Find the absolute value of the complex number.number.

i34 6.

24

23

16 9

255

1.4 Use the Complex Plane

Pg. 19, 1.4 #1-24