Aims: To know what the complex number i is. To be able to simplify complex numbers. To be able to add, subtract and multiply complex numbers. To know what.

Slides:

Advertisements

Similar presentations

Operations with Complex Numbers

Advertisements

Complex Numbers.

Complex Numbers - Day 1 My introduction Syllabus

Warm-upAnswers Compute (in terms of i) _i, -1, -i, 1.

Section 5.4 Imaginary and Complex Numbers

1.3 Complex Number System.

Section 3.2 Beginning on page 104

Warm-Up Exercises ANSWER ANSWER x =

5.7 Complex Numbers 12/17/2012.

§ 7.7 Complex Numbers. Blitzer, Intermediate Algebra, 4e – Slide #94 Complex Numbers The Imaginary Unit i The imaginary unit i is defined as The Square.

2.5 Introduction to Complex Numbers 11/7/2012. Quick Review If a number doesn’t show an exponent, it is understood that the number has an exponent of.

5-9 Operations with Complex Numbers Warm Up Lesson Presentation

Imaginary and Complex Numbers 18 October Question: If I can take the, can I take the ? Not quite…. 

Lesson 2.4 Read: Pages Page 137: #1-73 (EOO)

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”.

Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig. Aim: How do we add and subtract complex numbers? Do Now: Simplify:

Complex Numbers (and the imaginary number i)

Imaginary and Complex Numbers 15 October Question: If I can take the, can I take the ? Not quite…. 

Introduction to Complex Numbers Adding, Subtracting, Multiplying And Dividing Complex Numbers SPI Describe any number in the complex number system.

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,

Sullivan Algebra and Trigonometry: Section R.7 Rational Expressions

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

Algebra 2 Ch.9 Notes Page 64 P Add/Subtract Rational Expressions.

September 13, 2012 Working with Integers Warm-up: 1. Identify the property for: 3(1) = 3 2. Simplify: 6 + 3(9 – 1) + 2  Translate into an algebraic.

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

Complex Numbers Write imaginary numbers using i. 2.Perform arithmetic operations with complex numbers. 3.Raise i to powers.

Complex Numbers.  Numbers that are not real are called Imaginary. They use the letter i.  i = √-1 or i 2 = -1  Simplify each: √-81 √-10 √-32 √-810.

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

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

Warm-up Solve for x Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.

The properties of real numbers help us simplify math expressions and help us better understand the concepts of algebra.

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

Addition and Subtraction: Unlike Denominators  Mr. Peter Richard Is the Common Denominator needed in order to learn this Lesson!

Aims: To be to be able to classify types of numbers To be able to write a surd in its simplest form To be able to add, subtract and multiply surds SURDS.

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

Complex Numbers. Aim: Identify parts of complex numbers. Imaginary NumbersReal Numbers.

 Solve the equation.  1.) 3x = 23  2.) 2(x + 7) 2 = 16 Warm Up.

Multiply Simplify Write the expression as a complex number.

Holt McDougal Algebra 2 Operations with Complex Numbers Perform operations with complex numbers. Objective.

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.

ADDING AND SUBTRACTING MULTIPLYING AND DIVIDING REAL NUMBERS.

Simplify MultiplyDivide Add & Subtract Proportion.

The Complex Number System. 1. Write each expression as a pure imaginary number. (similar to p.537 #26)

Complex Numbers. Solve the Following 1. 2x 2 = 8 2. x = 0.

Algebra Operations with Complex Numbers. Vocabulary Imaginary Number i -

Complex Numbers Objectives Students will learn:

PreCalculus 1st Semester

Operations with Complex Numbers

Algebra 1 Section 2.3 Subtract real numbers

Section 5.9.B Complex Numbers.

Digital Lesson Complex Numbers.

6.7 Imaginary Numbers & 6.8 Complex Numbers

Imaginary Numbers.

Digital Lesson Complex Numbers.

Complex Numbers Any number in form a+bi, where a and b are real numbers and i is imaginary. What is an imaginary number?

Sec Math II Performing Operations with Complex Numbers

5-4 Operations with Complex Numbers SWBAT

Adding AND Subtracting Rational Expressions

College Algebra Chapter 1 Equations and Inequalities

1.2 Adding And Subtracting Complex Numbers

1.2 Adding And Subtracting Complex Numbers

Homework Corrections (page 1 of 2) A#13 / 1-1 Homework Worksheet

Digital Lesson Complex Numbers.

Class Greeting.

Warm-Up #9 Find the discriminant and determine the number of real solutions. Then solve. 1)

Warm-ups: Simplify the following

Binomial Radical Expressions

SECTION 1-5 : ADDING and SUBTRACTING REAL NUMBERS

Presentation transcript:

Aims: To know what the complex number i is. To be able to simplify complex numbers. To be able to add, subtract and multiply complex numbers. To know what a conjugate complex number is. Complex Numbers Lesson 1

Complex Numbers - Introduction Imaginary Numbers

Complex Numbers - Introduction Express in terms of i: 1.√(-64)2. √(-7) 3.√16 - √(-81) √(-25) 5.√(-100) - √(-49) Simplify 1.i 3 2. i 7 3.i i(2i – 3i 3 ) 5. (i + 2i 2 )(3 – i) 10 minutes – have a go!

Manipulation of Complex Numbers A complex number is Real partImaginary part Notes : 1.The complex conjugate of a complex number a + ib is a – ib 2.When a complex number is multiplied by its conjugate the answer is just REAL (a + ib)(a – ib) = 3.When adding complex numbers just add/subtract the real and imaginary parts separately. Eg. (2 + 3i) + (7 – 6i) =

Manipulation of Complex Numbers 4.Multiplying complex numbers just uses basic rules of algebra e.g. (4 – 3i)( i) =

Manipulation of Complex Numbers Mixed Example A complex number is z = 3 – 2i a)What is it’s conjugate, z*? b)What is the sum of z and z* ? c)What is z – z* d)What is the product of z and z* e)Can you make any general statements about parts b) to d) Do exercise 7A page mins have a go!

Finally!