Imaginary Numbers. You CAN have a negative under the radical. You will bring out an “i“ (imaginary).

Slides:

Advertisements

Similar presentations

Complex Numbers Section 0.7. What if it isnt Real?? We have found the square root of a positive number like = 4, Previously when asked to find the square.

Advertisements

Unit 4Radicals Complex numbers.

Operations with Complex Numbers

5.7.3 – Division of Complex Numbers. We now know about adding, subtracting, and multiplying complex numbers Combining like terms Reals with reals Imaginary.

Complex Numbers – Add, Subtract, Multiply, and Divide Addition of complex numbers is given by: Example 1:

Complex Numbers.

Skills Check Perform the indicated operation. Find the area & perimeter of the rectangle. 3. Perimeter = ____ 4. Area = ____ 2x + 1 2x – 3.

Complex Numbers.

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

1.3 Complex Number System.

§ 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.

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!

Warm up – Simplify. Questions over hw? Skills Check Perform the indicated operation. Find the area & perimeter of the rectangle. 3. Perimeter = ____.

7.3 – Binomial Radical Expressions. I. Adding and Subtracting Radical Expressions  Like Radicals – radicals that have the same radicand and index. 

Warm up. Questions over hw? Skills Check Simplify.

10.8 The Complex Numbers.

Unit 4 Operations & Rules

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.

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.

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.

SECTION 1.4 EXPONENTS. PRODUCT OF POWERS When you multiply two factors having the same base, keep the common base and add the exponents.

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.

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

7-7 Imaginary and Complex Numbers. Why Imaginary Numbers? n What is the square root of 9? n What is the square root of -9? no real number New type of.

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.

Complex Numbers Definitions Graphing 33 Absolute Values.

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

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.

Multiply the coefficients, the 2 and the -3 to get -6 a 3 * a 2 will be a 5, you add exponents when you multiply terms b 1 * b 4 will be b 5.

Complex Number System Reals Rationals (fractions, decimals) Integers (…, -1, -2, 0, 1, 2, …) Whole (0, 1, 2, …) Natural (1, 2, …) Irrationals.

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities Chapter 5 – Quadratic Functions and Inequalities 5.4 – 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.

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.

Complex Number System Reals Rationals (fractions, decimals) Integers (…, -1, -2, 0, 1, 2, …) Whole (0, 1, 2, …) Natural (1, 2, …) Irrationals.

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:

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

Imaginary Numbers Review Imaginary Numbers Quadratic Forms Converting Standard Form.

Complex Number 5-9. i = Imaginary Number i 2 = i 3 =i 2 i = -1*i = -i i 4 =i 2 i 2 = -1*-1 = 1 i 5 =i 4 i= 1*i= i i 6 =i 4 i 2 = 1*-1=-1 i 7 =i 4 i 3.

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

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

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,

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

Roots, Radicals, and Complex Numbers

PreCalculus 1st Semester

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

Warm up – Simplify.

6.7 Imaginary Numbers & 6.8 Complex Numbers

Rationalizing Imaginary and Complex Denominators

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

Roots, Radicals, and Complex Numbers

Complex numbers Math 3 Honors.

Section 4.6 Complex Numbers

College Algebra Chapter 1 Equations and Inequalities

1.2 Adding And Subtracting Complex Numbers

1.2 Adding And Subtracting Complex Numbers

Lesson 2.4 Complex Numbers

Skills Check 2x – 3 2x + 1 Perform the indicated operation.

Add and Subtract Radicals

Warm up – Simplify.

Express each number in terms of i.

1.2 Add & Subtract Complex Numbers

Add/Subt Complex Numbers

1.2 Add & Subtract Complex Numbers

Adding & subtracting Fractions With Common denominator.

Warm-ups: Simplify the following

Skills Check 2x – 3 2x + 1 Perform the indicated operation.

Presentation transcript:

Imaginary Numbers

You CAN have a negative under the radical. You will bring out an “i“ (imaginary).

Powers of i (The i Chart)

“I one, I one!!” Negatives in the middle. Reference

Simplify

Complex Number Standard Form (add this to your notes)

Add and Subtract Complex Numbers

Add/Subt Complex Numbers 1.Treat the i’s like variables 2.Combine like terms 3.Simplify (no powers of i higher than 1 are allowed) 4.Answer in standard form a + bi

Simplify

Multiplying Complex Numbers (no powers of i higher than 1 are allowed in your answer)

Multiplying Complex Numbers

Dividing Complex Numbers (no powers of i in the denominator are allowed in your answer)

What is a Conjugate? Example: (2 – 4i)

17. Dividing – Multiply top & bottom by the Conjugate

18. Dividing – Multiply top & bottom by the Conjugate