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.

Slides:

Advertisements

Similar presentations

Section 1.4 Complex Numbers

Advertisements

COMPLEX NUMBERS Objectives

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.

Complex Numbers The imaginary number i is defined as so that Complex numbers are in the form a + bi where a is called the real part and bi is the imaginary.

If you need to hear it and go through it with me, go to the “LINKS” section of my webpage and open it up there!!

solution If a quadratic equation is in the form ax 2 + c = 0, no bx term, then it is easier to solve the equation by finding the square roots. Solve.

EXAMPLE 1 Solve quadratic equations Solve the equation. a. 2x 2 = 8 SOLUTION a. 2x 2 = 8 Write original equation. x 2 = 4 Divide each side by 2. x = ±

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

1.3 Complex Number System.

Notes Over 5.4 Imaginary Numbers.

Section 2-5 Complex Numbers.

Sec 3.4 & Sec 3.5 Complex Numbers & Complex Zeros

Good Morning! Please get the e-Instruction Remote with your assigned Calculator Number on it, and have a seat… Then answer this question by aiming the.

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

Objectives Define and use imaginary and complex numbers.

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.

Section 2.2 The Complex Numbers.

Section 3.2 Beginning on page 104

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

Warm-Up Exercises ANSWER ANSWER x =

Do you remember… How do you simplify radicals? What happens when there is a negative under the square root? What is i? What is i 2 ? How do you add or.

Complex Numbers and Roots

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!

Negative Exponents SWBAT express powers with negative exponents as decimals; express decimals as powers with negative exponents; simplify expressions with.

Objectives Define and use imaginary and complex numbers.

EXAMPLE 2 Rationalize denominators of fractions Simplify

2.13 Warm Up x² - 2x + 15 = 0; 3 x² + 3x – 4 = 0; 1

Using square roots to solve quadratic equations. 2x² = 8 22 x² = 4 The opposite of squaring a number is taking its square root √ 4= ± 2.

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.

Divide. Evaluate power – 3 = – 3 EXAMPLE – 3 = 3 2 – – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.

1. 2. * Often times we are not able to a quadratic equation in order to solve it. When this is the case, we have two other methods: completing the square.

Imaginary and Complex Numbers Negative numbers do not have square roots in the real-number system. However, a larger number system that contains the real-number.

5.3 Factoring Quadratic Function 12/7/2012. are the numbers you multiply together to get another number: 3 and 4 are factors of 12, because 3x4=12. 2.

5.3 Solving Quadratic Functions with Square Roots Step 1: Add or subtract constant to both sides. Step 2: Divide or multiply coefficient of “x” to both.

Holt McDougal Algebra Complex Numbers and Roots 2-5 Complex Numbers and Roots Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation.

Chapter 5.9 Complex Numbers. Objectives To simplify square roots containing negative radicands. To solve quadratic equations that have pure imaginary.

Warm-Up Solve Using Square Roots: 1.6x 2 = x 2 = 64.

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

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities Chapter 5 – Quadratic Functions and Inequalities 5.4 – Complex Numbers.

Section 8.7 Complex Numbers. Overview In previous sections, it was not possible to find the square root of a negative number using real numbers: is not.

Honors Pre-Calculus Appendix A7 Complex Numbers. Objectives Add, Subtract, Multiply, and Divide Complex Numbers Graph Complex Numbers Solve Quadratic.

Chapter 4.6 Complex Numbers. Imaginary Numbers The expression does not have a real solution because squaring a number cannot result in a negative answer.

1-2 Order of Operations Objective: Use the order of operations to evaluate expressions.

Mrs. Rivas International Studies Charter School. Bell Ringer Translation is 4 units right.

Section 2.5 – Quadratic Equations

Simplify each expression.

Complex Numbers.

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

EXAMPLE 2 Rationalize denominators of fractions Simplify

Objectives Define and use imaginary and complex numbers.

Simplify each expression.

Solve a quadratic equation

6.7 Imaginary Numbers & 6.8 Complex Numbers

(Sections 4-5 pt. 1 & 2, 4-6 pt. 1, 4-7, 4-8 pt. 1 & 2)

Solving Quadratic Equations by finding Square Roots

Complex Numbers and Solving Equations

Complex Numbers Using Complex Conjugates in dividing complex numbers and factoring quadratics -- Week 15 11/19.

Section 9.4 Day 1 Solving Quadratic Equations by Completing the Square

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

Simplify each expression.

Section 9.4 Day 1 Solving Quadratic Equations by Completing the Square

Notes Over 9.1 Finding Square Roots of Numbers

Warm Up #3 Find the exact value. 2. –√ √49 ANSWER –12 7 ANSWER

4.5: Completing the square

Warm-Up Set 1: Factor. 1) x2 + 6x + 9 2) x2 - 10x + 25 Set 2: Factor.

Complex Numbers and Solving Equations

Notes Over Using Radicals

Complex Numbers and Roots

Equations and Exponents

Presentation transcript:

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. Add, subtract, multiply, and divide two complex numbers. Solve a quadratic equation with complex solutions.

Vocabulary complex number complex conjugate

Rewrite the following square root so that there is no longer a negative sign under the square root symbol.

Evaluate the expression

Multiply the following two numbers together.

Find the complex conjugate of each of the following:

Multiply the following two numbers together.

Evaluate the expression

Solve the equation: