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

Slides:



Advertisements
Similar presentations
5.4 Complex Numbers (p. 272).
Advertisements

4.6 Perform Operations with Complex Numbers
Win Our Money. For 100 Points What is the x and y intercept of 2x + 3y = 12 X-int = 6 ; y-int = 4.
= 9 = 8 = 12 = 19 = 2 = 3 = 17 = 5 = 11 = 5.
Graph an equation of a parabola
Imaginary and Complex Numbers. The imaginary number i is the square root of -1: Example: Evaluate i 2 Imaginary Numbers.
5-6 Complex Numbers.
Section 2-5 Complex Numbers.
5.4 Complex Numbers By: L. Keali’i Alicea. Goals 1)Solve quadratic equations with complex solutions and perform operations with complex numbers. 2)Apply.
Solve the equation. 2(x + 7)2 = 16.
Warm Up #3 Find the exact value. 2. –√ √49 ANSWER –12 7 ANSWER
Warm-Up Exercises ANSWER ANSWER x =
5.7 Complex Numbers 12/17/2012.
Precalculus Mr. Ueland 2 nd Period Rm 156. Today in PreCalculus Announcements/Prayer New material: Sec 2.5b, “Complex Numbers” Continue working on Assignment.
Objectives of this Section Graph Inequalities Find Distance on the Real Number Line Evaluate Algebraic Expressions Determine the Domain of a Variable Use.
How do I solve absolute value equations and inequalities?
1 C ollege A lgebra Linear and Quadratic Functions (Chapter2) 1.
How do I solve exponential equations and inequalities?
2.4 Graphs of Functions The graph of a function is the graph of its ordered pairs.
Section 9-5 Hyperbolas. Objectives I can write equations for hyperbolas I can graph hyperbolas I can Complete the Square to obtain Standard Format of.
2.13 Use Square Roots to Solve Quadratics Example 1 Solve quadratic equations Solution Write original equation. 5 Solve the equation. Add __ to each side.
Lesson Opener. 2-1 The Real Number Line Real Numbers = the set of all positive and negative numbers and zero –The point labeled zero is the ORIGIN.
2.8B Graphing Absolute Value Inequalities in the Coordinate Plane 1. Find location of the absolute value “V”  a I x – h I + k 2. Determine if graph is.
1) Identify the domain and range InputOutput ) Graph y = -2x Domain = -1, 2, 5 & 6 Range = -2 & 3.
Complex Numbers Definitions Graphing 33 Absolute Values.
1. Simplify 3 4 – ANSWER 11 Solve the equation. 2. 3x2 + 8 = 23 ANSWER
How do graph piecewise functions? 2.5 Use Piecewise Functions Example 1 Evaluate a piecewise function Evaluate the function when x = 3. Solution Because.
How do I graph and write absolute value functions?
How do I graph and use exponential growth and decay functions?
How do I use the imaginary unit i to write complex numbers?
5.4 – Complex Numbers. What is a Complex Number??? A complex number is made up of two parts – a real number and an imaginary number. Imaginary numbers.
Chapter 4 Section 8 Complex Numbers Objective: I will be able to identify, graph, and perform operations with complex numbers I will be able to find complex.
Aim: What is the complex number? Do Now: Solve for x: 1. x 2 – 1 = 0 2. x = 0 3. (x + 1) 2 = – 4 Homework: p.208 # 6,8,12,14,16,44,46,50.
5-6 Complex Numbers Part 1 Big Idea: Identify and graph complex numbers.
How do I find the inverse of functions? 4.3 Use Inverse Functions Inverse Functions Functions f and g are inverse functions of each other provided: The.
GeometryGeometry Equations of Circles Section 11.7.
Algebra 1 Section 2.1 Graph and order real numbers Find absolute values and opposites The numbers used in algebra 1 are real numbers. They include whole.
Simplify. Complex Numbers Complex Numbers Intro Definition of Pure Imaginary Numbers: For any positive real number, “b” Where i is the imaginary unit.
Warm-Up Exercises 1. Identify the axis of symmetry for the graph of y = 3x 2. ANSWER x = 0 2. Identify the vertex of the graph of y = 3x 2. ANSWER (0,
Add ___ to each side. Example 1 Solve a radical equation Solve Write original equation. 3.5 Solve Radical Equations Solution Divide each side by ___.
ALGEBRA TWO CHAPTER FIVE QUADRATIC FUNCTIONS 5.4 Complex Numbers.
WARM UP 3 SOLVE THE EQUATION. (Lesson 3.6) 1. x + 9 = x – 5 = x - 8 = 2.
Graph Rational Numbers on a Coordinate Plane…
Logarithmic Functions
Add and subtract complex numbers
4.4: Complex Numbers -Students will be able to identify the real and imaginary parts of complex numbers and perform basic operations.
8.3 Polar Form of Complex Numbers
Conjugates & Absolute Value & 14
1. Simplify 3 4 – ANSWER 11 Solve the equation. 2. 3x2 + 8 = 23 ANSWER
Solve a quadratic equation
(Sections 4-5 pt. 1 & 2, 4-6 pt. 1, 4-7, 4-8 pt. 1 & 2)
Complex Numbers.
Complex Numbers and Roots
The Coordinate Plane Chapter 2 Integers pg. 88.
Imaginary Numbers.
4.6 Complex Numbers (p. 275).
Chapter 5 Quadratics: 5. 3 Square Roots, 5. 4 Complex Numbers, & 5
Lesson 2.1 How do you order integers?
4.6 Perform Operations with Complex Numbers
Day 2 Write in Vertex form Completing the Square Imaginary Numbers Complex Roots.
4.1 – plotting points Textbook pg. 61 Objective:
WARM UP Evaluate the expression Simplify the Expression
0-2 Real Numbers.
Complex Numbers What you’ll learn
Warm Up #3 Find the exact value. 2. –√ √49 ANSWER –12 7 ANSWER
Exercise Every positive number has how many real square roots? 2.
Warm-Up Set 1: Factor. 1) x2 + 6x + 9 2) x2 - 10x + 25 Set 2: Factor.
Section – Complex Numbers
Complex Numbers.
How do I add and subtract complex numbers?
Presentation transcript:

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

1.4 Use the Complex Plane Example 1 Plot the complex numbers Plot the complex numbers in the same complex plane. a.To plot 2 + 4i, start at the origin, move 2 units _____, then move 4 units ___. right up b.To plot 1  3i, start at the origin, move 1 unit _____, then move 3 units ______. right down c.To plot  4  4i, start at the origin, move 4 units _____, then move 4 units ____. left up 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 Plane Checkpoint. Complete the following exercise. Plot the complex numbers in the same plane.

1.4 Use the Complex Plane Example 2 Find the absolute values of complex numbers Find the absolute value of the complex number. Solution Definition of _______________. Evaluate powers. Simplify.

1.4 Use the Complex Plane Example 2 Find the absolute values of complex numbers Find the absolute value of the complex number. Solution Definition of absolute value. Evaluate powers. Simplify.

Evaluate ______________. 1.4 Use the Complex Plane Example 2 Find the absolute values of complex numbers Find the absolute value of the complex number. Solution Definition of absolute value. Evaluate powers. Simplify.

Evaluate square root. 1.4 Use the Complex Plane Example 2 Find the absolute values of complex numbers Find the absolute value of the complex number. Solution Definition of absolute value. Evaluate powers. Simplify.

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

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

1.4 Use the Complex Plane Pg. 19, 1.4 #1-24