Section 1.4 Complex Numbers

Slides:

Advertisements

Similar presentations

Section 7.7 Complex Numbers.

Advertisements

Complex Numbers; Quadratic Equations in the Complex Number System

Complex Numbers Advanced Math Topics Mrs. Mongold.

§ 7.7 Complex Numbers.

Adapted from Walch Eduation 4.3.4: Dividing Complex Numbers 2 Any powers of i should be simplified before dividing complex numbers. After simplifying.

2.2 Complex Numbers Fri Feb 20 Do Now 1) 2x^2 -8 = 0 2) (sinx)^2 – 2sinx + 1 = 0.

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.

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

Imaginary and Complex Numbers. The imaginary number i is the square root of -1: Example: Evaluate i 2 Imaginary Numbers.

Section 5.4 Imaginary and Complex Numbers

Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra Complex Numbers Standard form of a complex number is: a + bi. Every complex polynomial function.

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

Notes Over 5.4 Imaginary Numbers.

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

Section 2.2 The Complex Numbers.

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

Equations and Inequalities

§ 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.

§ 7.7 Complex Numbers. Blitzer, Intermediate Algebra, 5e – Slide #3 Section 7.7 Complex Numbers The Imaginary Unit i The imaginary unit i is defined.

1.4 – Complex Numbers. Real numbers have a small issue; no symmetry of their roots – To remedy this, we introduce an “imaginary” unit, so it does work.

10.8 The Complex Numbers.

Complex Zeros; Fundamental Theorem of Algebra

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”.

RATIONAL EXPRESSIONS AND FUNCTIONS, RADICALS, AND RATIONAL EXPONENTS College Algebra.

Ch 2.5: The Fundamental Theorem of Algebra

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

Copyright © 2011 Pearson Education, Inc. Complex Numbers Section P.7 Prerequisites.

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.

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.

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

Complex Numbers Definitions Graphing 33 Absolute Values.

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

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

Chapter 2 Section 4 Complex Numbers.

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

Complex Numbers Dividing Monomials Dividing Binomials 33 Examples.

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

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.

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

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.

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:

Complex Numbers C.A-1.5. Imaginary numbers i represents the square root of – 1.

The imaginary unit i is defined as Furthermore.

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

Algebra 2. Solve for x Algebra 2 (KEEP IN MIND THAT A COMPLEX NUMBER CAN BE REAL IF THE IMAGINARY PART OF THE COMPLEX ROOT IS ZERO!) Lesson 6-6 The Fundamental.

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

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

Section 2.5 – Quadratic Equations

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

2.1 Complex Numbers.

Dividing & Solving Equations With Complex Numbers

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

Section 2.1 Complex Numbers

Section 1.4 Complex Numbers

Ch 6 Complex Numbers.

Roots, Radicals, and Complex Numbers

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

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

College Algebra Chapter 1 Equations and Inequalities

Imaginary root Reference book: Algebra & Trigonometry, M. Sullivan.

Multiplication and Division Property of Radicals

Section 10.7 Complex Numbers.

Multiplying and Dividing Rational Expressions

Complex Number.

7.7 Complex Numbers.

Presentation transcript:

Section 1.4 Complex Numbers

The Imaginary Unit i

Example Express as a multiple of i:

Operations with Complex Numbers

Example Perform the indicated operation:

Example Perform the indicated operation:

Complex Conjugates and Division

Using complex conjugates to divide complex numbers

Example Divide and express the result in standard form:

Example Divide and express the result in standard form:

Roots of Negative Numbers

Example Perform the indicated operations and write the result in standard form:

Example Perform the indicated operations and write the result in standard form:

Example Perform the indicated operations and write the result in standard form:

Find the product. (a) (b) (c) (d)

Perform the indicated operation. (b) (c) (d)