5.6 Complex Numbers Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. Warm-up (IN)

Slides:

Advertisements

Similar presentations

Quadratic Equations and Complex Numbers

Advertisements

Finding Complex Roots of Quadratics

Chapter 5 Section 4: Complex Numbers. VOCABULARY Not all quadratics have real- number solutions. For instance, x 2 = -1 has no real-number solutions because.

7.4 The Quadratic Formula and the Discriminant

Complex Numbers Section 2.1. Objectives Rewrite the square root of a negative number as a complex number. Write the complex conjugate of a complex number.

5.3 Complex Numbers; Quadratic Equations with a Negative Discriminant.

5.8 Quadratic Inequalities

Complex Number A number consisting of a real and imaginary part. Usually written in the following form (where a and b are real numbers): Example: Solve.

4.8 Quadratic Formula and Discriminant

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Notes Over 5.4 Imaginary Numbers.

Sullivan Algebra and Trigonometry: Section 1.3 Quadratic Equations in the Complex Number System Objectives Add, Subtract, Multiply, and Divide Complex.

5.6 Complex Numbers. Solve the following quadratic: x = 0 Is this quadratic factorable? What does its graph look like? But I thought that you could.

4.8: Quadratic Formula HW: worksheet

Sec 5.6 Quadratic Formula & Discriminant Quadratic Formula (Yes, it’s the one with the song!) If ax 2 + bx + c = 0 and a ≠ 0, then the solutions (roots)

Warm-Up: December 13, 2011  Solve for x:. Complex Numbers Section 2.1.

Warm up – Solve by Taking Roots. Solving by the Quadratic Formula.

Solving Quadratic Equations – The Discriminant The Discriminant is the expression found under the radical symbol in the quadratic formula. Discriminant.

5.4 Complex Numbers Until now, you have always been told that you can’t take the square root of a negative number. If you use imaginary units, you can!

Imaginary Number: POWERS of i: Is there a pattern?

5.6 Quadratic Equations and Complex Numbers

5.6 Quadratic Equations and Complex Numbers

Solving quadratic equations A root, or solution of a quadratic equation is the value of the variable that satisfies the equation. Three methods for solving.

Goals: To solve quadratic equations by using the Quadratic Formula.

5.5 Quadratic Formula Warm-up (IN) Learning Objective: To use the quadratic formula to find real roots of quadratic equations and to use the roots to find.

5.4 Complex Numbers. Let’s see… Can you find the square root of a number? A. E.D. C.B.

5.6 Quadratic Formula & Discriminant

Pre-Calculus Section 1.5 Equations Objectives: To solve quadratics by factoring, completing the square, and using the quadratic formula. To use the discriminant.

Do Now : Evaluate when x = 6, y = -2 and z = The Quadratic Formula and the Discriminant Objectives Students will be able to: 1)Solve quadratic.

4.8 Do Now: practice of 4.7 The area of a rectangle is 50. If the width is x and the length is x Solve for x by completing the square.

4.6 Perform Operations With Complex Numbers. Vocabulary: Imaginary unit “i”: defined as i = √-1 : i 2 = -1 Imaginary unit is used to solve problems that.

The Quadratic Formula & Discriminant Essential question – How do you solve a quadratic equation using the Quadratic Formula?

5.6 – Quadratic Equations and Complex Numbers Objectives: Classify and find all roots of a quadratic equation. Graph and perform operations on complex.

Pre-Calculus Lesson 5: Solving Quadratic Equations Factoring, quadratic formula, and discriminant.

Quadratic Formula You can use this formula to find the solutions(roots) to a quadratic equation. This formula can be broken up into 2 parts: b 2 – 4ac.

CPM Section 9.4A Quadratic Formula. Thus far we have considered two methods for solving quadratic function- factoring and using the square root property.

Wed 11/4 Lesson 4 – 7 Learning Objective: To solve using quadratic equations Hw: Lesson 4 – 7 WS.

4.2 Quadratic Functions Objective: Solve quadratic equations. Use the discriminant to describe the roots of a quadratic equation.

5-7: COMPLEX NUMBERS Goal: Understand and use complex numbers.

Notes Over 5.6 Quadratic Formula

Chapter 4: Polynomial and Rational Functions. 4-2 Quadratic Equations For a quadratic equation in the form ax 2 + bx + c = 0 The quadratic Formula is.

9.2 THE DISCRIMINANT. The number (not including the radical sign) in the quadratic formula is called the, D, of the corresponding quadratic equation,.

5.6 – Quadratic Equations and Complex Numbers Objectives: Classify and find all roots of a quadratic equation. Graph and perform operations on complex.

SAT Problem of the Day. 5.6 Quadratic Equations and Complex Numbers 5.6 Quadratic Equations and Complex Numbers Objectives: Classify and find all roots.

Warm-Up Use the quadratic formula to solve each equation. 6 minutes 1) x x + 35 = 02) x = 18x 3) x 2 + 4x – 9 = 04) 2x 2 = 5x + 9.

Table of Contents Solving Quadratic Equations – The Discriminant The Discriminant is the expression found under the radical symbol in the quadratic formula.

Imaginary Numbers Review Imaginary Numbers Quadratic Forms Converting Standard Form.

January 17, 2012 At the end of the today, you will be able to work with complex numbers. Warm-up: Correct HW 2.3: Pg. 160 # (2x – 1)(x + 2)(x.

Lesson 6.5: The Quadratic Formula and the Discriminant, pg. 313 Goals: To solve quadratic equations by using the Quadratic Formula. To use the discriminant.

Section 2.5 – Quadratic Equations

How do I solve quadratic equations using Quadratic Formula?

Do Now Use the standard form of a quadratic equation to find the a, b and c of each equation. ax2 + bx + c = 0 x2 – 6x + 10 = 0 2x2 + 3x + 4 = 0 x2 –

4.6 Quadratic formula.

The Quadratic Formula & Discriminant

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

4.8 Complex Numbers Learning goals

The QUADRATIC Discriminant.

4.6 Quadratic formula.

Solve x2 + 2x + 24 = 0 by completing the square.

Section 5.8 The Quadratic Formula

5.6 The Quadratic Formula and the Discriminant

4.8 The Quadratic Formula and the Discriminant

Unit 7 Day 4 the Quadratic Formula.

Section 5.8 The Quadratic Formula

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Quadratic Formula & the Discriminant

Using the Quadratic Formula to Solve Quadratic Equations

Directions- Solve the operations for the complex numbers.

Presentation transcript:

5.6 Complex Numbers Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. Warm-up (IN) Use the quadratic formula to solve each equation.

Notes Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. **Discriminant - then there are 2 real solutions then there is 1 real solution then there are 2 imaginary solutions Determines the # of solutions

Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. EX 1 – find the discriminant and determine the # of solutions: 1 real solution 2 real solutions

Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. 2 imaginary solutions Can’t take of a negative #! solve So…we use the imaginary unit, i

Learning Objective: To identify and perform transformations and to describe movement and patterns in real life situations. EX 2 – Solve: Complex number in standard form: real # imaginary #

Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. EX 3 – Write the expression as a complex number in standard form:

Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. EX 4 – multiply:

Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. are called conjugates i cancels out!

Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. EX 5 – Divide: So…multiply by the conjugate! It cancels out the i! Can’t have i in the denominator!

Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers.

HW – p. 320 #15-33 (mult of 3), (mult of 3), 64,65,68 Out – What can the discriminant tell you about the solutions of a quadratic equation. Summary – I have a question about…or, I get… POW!!