Complex Numbers We haven’t been allowed to take the square root of a negative number, but there is a way: Define the imaginary number For example,

Slides:

Advertisements

Similar presentations

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

Advertisements

Complex Numbers.

Complex Numbers.

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

Section 5.4 Imaginary and Complex Numbers

Lesson 1-5 The Complex Numbers. Objective: Objective: To add, subtract, multiply, and divide complex numbers.

1.3 Complex Number System.

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.

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

10.8 The Complex Numbers.

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.

6.3 Binomial Radical Expressions P You can only use this property if the indexes AND the radicands are the same. This is just combining like terms.

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.

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.

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.

4-8 Complex Numbers Today’s Objective: I can compute with complex numbers.

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

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

Drill #81: Solve each equation or inequality

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.

1.4 Complex Numbers Review radicals and rational exponents. We need to know how to add, subtract, multiply and divide complex numbers.

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

2.1 Complex Numbers. The Imaginary Unit Complex Numbers the set of all numbers in the form with real numbers a and b; and i, (the imaginary unit), is.

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

Lesson 1.8 Complex Numbers Objective: To simplify equations that do not have real number solutions.

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.

Pre Clac Chapter 2 Section 4. Imaginary #’s Let’s pretend that x = 0 had a solution That would mean x 2 = -1 That can’t be… if you square a number.

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.

Simplifying Radicals 6/3/ :02 AM Simplifying Radicals.

Roots, Radicals, and Complex Numbers

Chapter 2 – Polynomial and Rational Functions

Complex & Imaginary Numbers

Complex Numbers Objectives Students will learn:

PreCalculus 1st Semester

Lesson 5-6 Complex Numbers.

Complex Numbers Imaginary Numbers Vectors Complex Numbers

Operations with Complex Numbers

Digital Lesson Complex Numbers.

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

6.7 Imaginary Numbers & 6.8 Complex Numbers

In other words, exponents that are fractions.

Imaginary Numbers.

Digital Lesson Complex Numbers.

Complex Numbers and Solving Equations

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

Sec Math II Performing Operations with Complex Numbers

Roots, Radicals, and Complex Numbers

Complex Numbers Objectives Students will learn:

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

Simplifying Radicals 2/18/2019 3:50 PM Simplifying Radicals.

1.2 Adding And Subtracting Complex Numbers

Sec. 1.5 Complex Numbers.

1.2 Adding And Subtracting Complex Numbers

Lesson 2.4 Complex Numbers

Section 10.7 Complex Numbers.

Complex Numbers include Real numbers and Imaginary Numbers

Express each number in terms of i.

Digital Lesson Complex Numbers.

5.4 Complex Numbers.

Introduction to Complex Numbers

Complex Numbers and Solving Equations

7.7 Complex Numbers.

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.

Presentation transcript:

Complex Numbers We haven’t been allowed to take the square root of a negative number, but there is a way: Define the imaginary number For example,

Ex. Simplify a) b)

A complex number in standard form looks like: a + bi, where a and b are real numbers. In the complex number 5 + 3i, 5 is the real part 3 is the imaginary part  If b = 0, it is a real number

Add and subtract by combining like terms Ex. Write as a complex number in standard form.

Multiply by foiling  don’t forget i 2 = -1 Ex. Simplify

Ex. Write as a complex number in standard form.

If a complex number looks like a + bi, its complex conjugate will be a – bi. Ex. Write the complex conjugate of 6 – 5i, then multiply them.  The product of a complex number and its conjugate is always a real number  This can be used to rationalize the denominator

Ex. Write as a complex number in standard form.

Ex. Evaluate i 13