Complex Numbers Advanced Math Topics Mrs. Mongold.

Slides:

Advertisements

Similar presentations

Quadratic Equations and Complex Numbers

Advertisements

Section 1.4 Complex Numbers

Complex Numbers.

7.5 – Rationalizing the Denominator of Radicals Expressions

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

SQUARE ROOT METHOD. Simplify Radicals A. Single Ex.

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

Section 5.4 Imaginary and Complex Numbers

RADICAL EXPRESSIONS.

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

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.

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

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?

10.8 The Complex Numbers.

Identify the perfect square in each set , 81, 27, , 99, 8, , 84, 12, , 216, 196, 72 Find the Prime Factorization of.

9.2 Students will be able to use properties of radicals to simplify radicals. Warm-Up  Practice Page 507 – 508 l 41, 42, 45, 46, 55, 57, 59, 65.

3.6 Solving Quadratic Equations

Rationalizing the Denominator. Essential Question How do I get a radical out of the denominator of a fraction?

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

Aim: How do we multiply or divide complex numbers? Do Now: 1. Multiply: 2. Multiply: 3. Multiply: 6 + 7x + 2x i HW: p.216 # 26,30,32,36,38,40,50,52.

Complex Numbers 2-4.

Day Problems Simplify each expression – – (-8.4) 3. Evaluate each expression for a = -2, b = 3.5, and c = a – b + c5. |c + a + 5|

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.

1 What you will learn  Lots of vocabulary!  A new type of number!  How to add, subtract and multiply this new type of number  How to graph this new.

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

Complex Number System Adding, Subtracting, Multiplying and Dividing Complex Numbers Simplify powers of i.

Do Now What is the exact square root of 50? What is the exact square root of -50?

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.

Complex Numbers Add and Subtract complex numbers Multiply and divide complex numbers.

Complex Numbers Definitions Graphing 33 Absolute Values.

SIMPLIFYING RADICAL EXPRESSIONS

Chapter 9 Section 4 Dividing Square Roots. Learning Objective 1.Understand what it means for a square root to be simplified 2.Use the Quotient Rule to.

Complex Numbers warm up 4 Solve the following Complex Numbers Any number in form a+bi, where a and b are real numbers and i is imaginary. What is an.

To divide radicals: divide the coefficients divide the radicands if possible rationalize the denominator so that no radical remains in the denominator.

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.

Chapter 2 Section 4 Complex Numbers.

Chapter 1 Equations and Inequalities Copyright © 2014, 2010, 2007 Pearson Education, Inc Complex Numbers.

Multiplication and Division Property of Inequalities When c is positive, if a > b, then a c > b c When c is negative, if a > b, then a c < b c.

Complex Numbers Dividing Monomials Dividing Binomials 33 Examples.

Complex Numbers n Understand complex numbers n Simplify complex number expressions.

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

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.

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

FIND SQUARE ROOTS PERFORM OPERATIONS WITH PURE IMAGINARY NUMBERS. PERFORM OPERATIONS WITH COMPLEX NUMBERS. 5.4 Complex Numbers.

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

Algebra Operations with Complex Numbers. Vocabulary Imaginary Number i -

Section 2.4 – The Complex Numbers. The Complex Number i Express the number in terms of i.

11.4 Multiply & Divide Radical Expressions

EXAMPLE 2 Rationalize denominators of fractions Simplify

Copyright © Cengage Learning. All rights reserved.

Aim: How do we multiply or divide complex numbers? Do Now:

Operations with Complex Numbers

6.7 Imaginary Numbers & 6.8 Complex Numbers

Imaginary Numbers.

Unit 4 Lesson 1: Completing the square

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

Complex numbers Math 3 Honors.

Unit 11 Math-2 (Honors) 11.1: Dividing Square root numbers

Lesson 2.4 Complex Numbers

Imaginary Numbers though they have real world applications!

10-1 Simplifying Radicals

7.7 Complex Numbers.

Dividing Radical Expressions

Complex Numbers Multiply

Presentation transcript:

Complex Numbers Advanced Math Topics Mrs. Mongold

Can you find the square root of a number? Lets see…

What about the sqare root of a number that isnt a perfect square?

So Lets Review… To find the square root of negative numbers you need to use imaginary numbers. i is the imaginary unit i 2 = -1 i =

What about the square root of a negative number?

The Square Root Property For any real number n, if x 2 =n, then x = ±

Lets Practice With i Simplify -2i (7i) (2 – 2i) + (3 + 5i) i 45 i 31

Solve 3x = 0 4x = 0 x 2 + 4= 0

More with Complex Numbers Multiply (3 + 4i) (3 – 4i) (1 – 4i) (2 + i) (1 + 3i) (7 – 5i) (2 + 6i) (5 – 3i)

More with Complex numbers Conjugate: a binomial with the opposite sign as the original binomial Given 2-i the conjugate is 2+i You use the conjugate to simplify a fraction containing imaginary numbers

Cant have i in the denominator Divide 3i 2 + 4i -2i 3 + 5i 2 + i 1 - i

More division 5 + i 2i 4 – i 5i

Homework Page 503/3-72 multiples of 3