Topic: about todays class Level: 2 (conversation )

Slides:

Advertisements

Similar presentations

7.5 – Rationalizing the Denominator of Radicals Expressions

Advertisements

Complex Numbers.

Section 7.8 Complex Numbers  The imaginary number i  Simplifying square roots of negative numbers  Complex Numbers, and their Form  The Arithmetic.

6.2 – Simplified Form for Radicals

Review and Examples: 7.4 – Adding, Subtracting, Multiplying Radical Expressions.

1.3 Complex Number System.

Honors Topics.  You learned how to factor the difference of two perfect squares:  Example:  But what if the quadratic is ? You learned that it was.

Objectives Define and use imaginary and complex numbers.

Warm-Up Exercises ANSWER ANSWER x =

Introduction Identities are commonly used to solve many different types of mathematics problems. In fact, you have already used them to solve real-world.

5.7 Complex Numbers 12/17/2012.

Complex Numbers and Roots

Objectives Define and use imaginary and complex numbers.

Objectives Define and use imaginary and complex numbers.

EXAMPLE 2 Rationalize denominators of fractions Simplify

1 Complex Numbers Digital Lesson. 2 Definition: Complex Number The letter i represents the numbers whose square is –1. i = Imaginary unit If a is a positive.

Section 7.7 Previously, when we encountered square roots of negative numbers in solving equations, we would say “no real solution” or “not a real number”.

3.6 Solving Quadratic Equations

5.6 Solving Quadratic Function By Finding Square Roots 12/14/2012.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 8 Rational Exponents, Radicals, and Complex Numbers.

5.7 Complex Numbers 12/4/2013. Quick Review If a number doesn’t show an exponent, it is understood that the number has an exponent of 1. Ex: 8 = 8 1,

Lesson 2.1, page 266 Complex Numbers Objective: To add, subtract, multiply, or divide complex numbers.

7.7 Complex Numbers. Imaginary Numbers Previously, when we encountered square roots of negative numbers in solving equations, we would say “no real solution”

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

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

NOTES 5.7 FLIPVOCABFLIPVOCAB. Notes 5.7 Given the fact i 2 = ________ The imaginary number is _____ which equals _____ Complex numbers are written in.

How do I use the imaginary unit i to write complex numbers?

5.9 Complex Numbers Objectives: 1.Add and Subtract complex numbers 2.Multiply and divide complex numbers.

5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify. Multiply. Express in terms of i.

6.6 – Complex Numbers Complex Number System: This system of numbers consists of the set of real numbers and the set of imaginary numbers. Imaginary Unit:

Multiply Simplify Write the expression as a complex number.

Section 8.5 and 8.6 Multiplying and Dividing Radicals/Solving Radical Equations.

Any questions about the practice? Page , 11, 13, 21, 25, 27, 39, 41, 53.

Add ___ to each side. Example 1 Solve a radical equation Solve Write original equation. 3.5 Solve Radical Equations Solution Divide each side by ___.

Section 2.5 – Quadratic Equations

Section 7.1 Rational Exponents and Radicals.

Imaginary & Complex Numbers

Simplify –54 by using the imaginary number i.

Simplify each expression.

EXAMPLE 2 Rationalize denominators of fractions Simplify

Objectives Define and use imaginary and complex numbers.

Imaginary & Complex Numbers

Simplify each expression.

Imaginary & Complex Numbers

Imaginary & Complex Numbers

6.7 Imaginary Numbers & 6.8 Complex Numbers

Equations with Radicals

Imaginary & Complex Numbers

Ch 6 Complex Numbers.

Imaginary & Complex Numbers

Roots, Radicals, and Complex Numbers

Imaginary & Complex Numbers

Complex Numbers and Roots

Simplify each expression.

Imaginary & Complex Numbers

Complex Numbers and Roots

Lesson 2.4 Complex Numbers

Multiplying, Dividing, and Simplifying Radicals

Section 10.7 Complex Numbers.

Imaginary Numbers though they have real world applications!

Topic: about todays class Level: 2 (conversation )

Complex Numbers and Roots

Complex Numbers and Roots

Topic: about todays class Level: 2 (conversation )

Topic: about todays class Level: 2 (conversation )

Complex Numbers and Roots

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

Lesson 5–5/5–6 Objectives Be able to define and use imaginary and complex numbers Be able to solve quadratic equations with complex roots Be able to solve.

Solve Quadratic Equations by Finding Square Roots Lesson 1.5

Complex Numbers and Roots

Presentation transcript:

Topic: about todays class Level: 2 (conversation ) Entering class room Conversation: ending Topic: about todays class Level: 2 (conversation ) Movement: go to asng. desk turn off cell phones/hats off/no food or drink get out pencil, paper and be ready to start at the end of t tardy bell

7.5 – Rationalizing the Denominator of Radicals Expressions Radical expressions, at times, are easier to work with if the denominator does not contain a radical. The process to clear the denominator of all radical is referred to as rationalizing the denominator

7.5 – Rationalizing the Denominator of Radicals Expressions

7.5 – Rationalizing the Denominator of Radicals Expressions

7.5 – Rationalizing the Denominator of Radicals Expressions If the denominator contains a radical and it is not a monomial term, then the use of a conjugate is required. Review: (x + 3)(x – 3)  x2 – 3x + 3x – 9  x2 – 9 (x + 7)(x – 7)  x2 – 7x + 7x – 49  x2 – 49

7.5 – Rationalizing the Denominator of Radicals Expressions If the denominator contains a radical and it is not a monomial term, then the use of a conjugate is required. conjugate

7.5 – Rationalizing the Denominator of Radicals Expressions conjugate

7.5 – Rationalizing the Denominator of Radicals Expressions conjugate

7.6 – Radical Equations and Problem Solving The Squaring Property of Equality: Examples:

7.6 – Radical Equations and Problem Solving Suggested Guidelines: 1) Isolate the radical to one side of the equation. 2) Square both sides of the equation. 3) Simplify both sides of the equation. 4) Solve for the variable. 5) Check all solutions in the original equation.

7.6 – Radical Equations and Problem Solving

7.6 – Radical Equations and Problem Solving

7.6 – Radical Equations and Problem Solving no solution

7.6 – Radical Equations and Problem Solving

7.6 – Radical Equations and Problem Solving

7.6 – Radical Equations and Problem Solving

7.6 – Radical Equations and Problem Solving

7.7 – Complex Numbers Complex Number System: This system of numbers consists of the set of real numbers and the set of imaginary numbers. Imaginary Unit: The imaginary unit is called i, where and Square roots of a negative number can be written in terms of i.        

Operations with Imaginary Numbers 7.7 – Complex Numbers The imaginary unit is called i, where and Operations with Imaginary Numbers             

7.7 – Complex Numbers The imaginary unit is called i, where and Numbers that can written in the form a + bi, where a and b are real numbers. 3 + 5i 8 – 9i –13 + i The Sum or Difference of Complex Numbers     

7.7 – Complex Numbers      

Multiplying Complex Numbers        

Multiplying Complex Numbers       

Dividing Complex Numbers Complex Conjugates: The complex numbers (a + bi) and (a – bi) are complex conjugates of each other and, (a + bi)(a – bi) = a2 + b2    

Dividing Complex Numbers Complex Conjugates: The complex numbers (a + bi) and (a – bi) are complex conjugates of each other and, (a + bi)(a – bi) = a2 + b2    

Dividing Complex Numbers Complex Conjugates: The complex numbers (a + bi) and (a – bi) are complex conjugates of each other and, (a + bi)(a – bi) = a2 + b2    

Independent study expectations Conversation: Yes Topic: lesson only Level: 1 Movement: turn in work only. Help: raise hand Cell Phones: no