COMPLEX NUMBERS AND POLAR FORM Section 10 3

COMPLEX NUMBERS AND POLAR FORM Section 10. 3 Pre-Calculus AB Pre. AP/Dual, Revised © 2014 Viet. dang@humble. k 12. tx. us 10/28/2021 9: 49 AM 10. 3 - Complex Numbers and Polar Form 1

REVIEW Solve, y = x 2 – 1 and graph on a coordinate plane 10/28/2021 9: 49 AM 10. 3 - Complex Numbers and Polar Form 2

REVIEW Solve, y = x 2 + 1 and graph on a coordinate plane 10/28/2021 9: 49 AM 10. 3 - Complex Numbers and Polar Form 3

THE COMPLEX PLANE Graphing the Complex Plane Imaginary Axis O 10/28/2021 9: 49 AM 10. 3 - Complex Numbers and Polar Form Real Axis 4

EXAMPLE 1 Graph each complex number: 2 – 3 i • 2 – 3 i 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 5

EXAMPLE 2 Graph each complex number: (2 – i)(2 + i) • 5 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 6

YOUR TURN Graph each complex number: 2 i (2 – i) • 2 + 4 i 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 7

ABSOLUTE VALUE OF COMPLEX NUMBERS 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 8

THE COMPLEX PLANE Graphing the Complex Plane Imaginary Axis O 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form Real Axis 9

EXAMPLE 3 Solve|3 + 4 i| 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 10

EXAMPLE 4 Solve |– 2 + 4 i| 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 11

YOUR TURN Solve |10 – 4 i| 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 12

POLAR FORM Identify the relationship of x, y, r, and θ in terms of trig functions 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 13

POLAR FORM Identify the relationship of x, y, r, and θ in terms of trig functions 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 14

POLAR FORM 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 15

STEPS IN CONVERTING IN POLAR FORM 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 16

EXAMPLE 5 • 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 17

EXAMPLE 6 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 18

YOUR TURN 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 19

EXAMPLE 7 • 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 20

EXAMPLE 7 • 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 21

EXAMPLE 8 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 22

YOUR TURN 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 23

ASSIGNMENT Page 642 1 -13 odd, 25 -30 all, 39, 40, 43, 45 Due Monday after break. Have a great Thanksgiving. 10/28/2021 9: 50 AM 10. 3 - Complex Numbers and Polar Form 24