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

Slides:

Advertisements

Similar presentations

Operations with Complex Numbers

Advertisements

Complex Numbers.

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

Objective Perform operations with complex numbers.

Daily Check: Perform the indicated operation. Find the area and perimeter of the box. 3. Perimeter = ____ 4. Area = ____ 2x+1 2x-3.

1.3 Complex Number System.

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

5-9 Operations with Complex Numbers Warm Up Lesson Presentation

Warm up. Questions over hw? Skills Check Simplify.

Unit 4 Operations & Rules

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

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.

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

Complex Numbers Definitions Graphing 33 Absolute Values.

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

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

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

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

5.7.2 – Complex Numbers. From yesterday, we learned the application of the imaginary unit i Used for problems such as; -5x 2 = 20.

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

Complex Numbers Simplifying Addition & Subtraction 33 Multiplication.

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,

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

Imaginary & Complex Numbers

Roots, Radicals, and Complex Numbers

Imaginary & Complex Numbers

Complex & Imaginary Numbers

With a different method

Imaginary & Complex Numbers

Complex Numbers.

PreCalculus 1st Semester

Imaginary & Complex Numbers

Operations with Complex Numbers

Warm up – Simplify.

Complex Numbers.

Imaginary Numbers.

4.6 Complex Numbers (p. 275).

Complex Numbers.

Math is about to get imaginary!

Imaginary & 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?

9-5 Complex Numbers.

Imaginary & Complex Numbers

Roots, Radicals, and Complex Numbers

Warm Up Take out your notes from last class and underline or highlight important information that you need to remember when solving and graphing quadratic.

Imaginary & Complex Numbers

Complex numbers Math 3 Honors.

Section 4.6 Complex Numbers

4.6 Perform Operations with Complex Numbers

College Algebra Chapter 1 Equations and Inequalities

Imaginary & Complex Numbers

Complex Number and Roots

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.

Section 10.7 Complex Numbers.

Warm up – Simplify.

4.6 Complex Numbers Algebra II.

Daily Check: Perform the indicated operation.

2.2 Solving Equations with Variables on Both Sides

Express each number in terms of i.

1.2 Add & Subtract Complex Numbers

Add/Subt Complex Numbers

5.4 Complex Numbers.

1.2 Add & Subtract Complex Numbers

Complex Numbers.

Presentation transcript:

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

Powers of i and Complex Operations

Add to the sheet “I one, I one!!” Negatives in the middle.

Try these!

Graphing in the Complex Plane

The Complex Plane

Identify the points A B D C

Add and Subtract Complex Numbers

Add/Subt Complex Numbers Treat the i’s like variables Combine the real parts then combine the imaginary parts Simplify (no powers of i higher than 1) Write your answer in standard form a + bi

Add/Subt Complex Numbers

Multiplying Complex Numbers

Multiplying Complex Numbers Treat the i’s like variables Change all imaginaries (i) that are not to the first power Simplify Write your answer in standard form a + bi

Multiplying Complex Numbers

Multiplying Complex Numbers

Multiplying Complex Numbers

Conjugates

Conjugate

Dividing Complex Numbers