6

Complex Numbers

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

Download PPT Report

Upload
megan-bryant
View
257
Download
5

Embed Size (px)

DESCRIPTION

Aim: Identify parts of complex numbers. Yesterday we looked at adding, subtracting, multiplying, and dividing imaginary numbers. A pure imaginary number has both a real number and an imaginary number. i 2i2i -5 i 3i√33i√3 3i23i2

Citation preview

Page 1: Complex Numbers. Aim: Identify parts of complex numbers. Imaginary NumbersReal Numbers

Complex Numbers

Page 2: Complex Numbers. Aim: Identify parts of complex numbers. Imaginary NumbersReal Numbers

Aim: Identify parts of complex numbers.

Imaginary Numbers

Real Numbers

Page 3: Complex Numbers. Aim: Identify parts of complex numbers. Imaginary NumbersReal Numbers

Aim: Identify parts of complex numbers.

Yesterday we looked at adding, subtracting, multiplying, and dividing imaginary numbers. A pure imaginary number has both a real number and an imaginary number.

i2i -5i

3i√3 3i2

Page 4: Complex Numbers. Aim: Identify parts of complex numbers. Imaginary NumbersReal Numbers

Aim: Identify parts of complex numbers.

Today we’re going to witness two worlds stand separated

+

ORcollide & unite.

Page 5: Complex Numbers. Aim: Identify parts of complex numbers. Imaginary NumbersReal Numbers

Aim: Identify parts of complex numbers.

7 + 2i 7 2i1 - 5i 1 -5i

8i 0 8i2 2 0i

Page 6: Complex Numbers. Aim: Identify parts of complex numbers. Imaginary NumbersReal Numbers

Aim: Identify parts of complex numbers.

Each world gets its own axis.

Every complex number has a position.

2 + 5i 2 - 5i -2 + 5i

-2 - 5i 5i 5

5i + 2

Complex Numbers 2-4. Imaginary Numbers 1.Designed so negative numbers can have square roots., i 2 = -1 2.Imaginary numbers consist of all numbers bi,

Complex Numbers 2-4. Imaginary Numbers 1.Designed so negative numbers can have square roots., i 2 = -1 2.Imaginary numbers consist of all numbers bi,

Documents

Use the imaginary unit i to write complex numbers. Add, subtract, and multiply complex numbers. Use complex conjugates to write the quotient of two complex

Use the imaginary unit i to write complex numbers. Add, subtract, and multiply complex numbers. Use complex conjugates to write the quotient of two complex

Documents

Imaginary & Complex Numbers Obj: Simplify expressions with imaginary numbers; re-write radicals as complex expressions. Why do imaginary numbers exists

Imaginary & Complex Numbers Obj: Simplify expressions with imaginary numbers; re-write radicals as complex expressions. Why do imaginary numbers exists

Documents

1.3 Complex Number System. Complex Numbers Numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit

1.3 Complex Number System. Complex Numbers Numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit

Documents

1 EXPLORATION: Classifying Numbers€¦ · 1 EXPLORATION: Classifying Numbers Complex Numbers Real Numbers Imaginary Numbers Rational Numbers Irrational Numbers Integers Whole Numbers

1 EXPLORATION: Classifying Numbers€¦ · 1 EXPLORATION: Classifying Numbers Complex Numbers Real Numbers Imaginary Numbers Rational Numbers Irrational Numbers Integers Whole Numbers

Documents

Operations with complex numbers - WordPress.com · Operations with complex numbers Book page 109 - 114 ©cgrahamphysics.com 2016. Equality •Two imaginary numbers are equal if and

Operations with complex numbers - WordPress.com · Operations with complex numbers Book page 109 - 114 ©cgrahamphysics.com 2016. Equality •Two imaginary numbers are equal if and

Documents

5.4 Imaginary and Complex Numbers - mrsespositomrsespositomath.weebly.com/uploads/3/8/1/7/38179709/5_4... · 2018. 10. 17. · Algebra 2 Trig Name_____ 5.4 Imaginary and Complex Numbers

5.4 Imaginary and Complex Numbers - mrsespositomrsespositomath.weebly.com/uploads/3/8/1/7/38179709/5_4... · 2018. 10. 17. · Algebra 2 Trig Name_____ 5.4 Imaginary and Complex Numbers

Documents

Secondary 2 lesson 3.3: Complex Numbers - Lehi …lehimath.weebly.com/.../3.3_complex_numbers_+,-____work.pdfSecondary 2 lesson 3.3: Complex Number +,-imaginary number numbers imaginary

Secondary 2 lesson 3.3: Complex Numbers - Lehi …lehimath.weebly.com/.../3.3_complex_numbers_+,-____work.pdfSecondary 2 lesson 3.3: Complex Number +,-imaginary number numbers imaginary

Documents

Chapter 5: Complex Numbers · 4 Day 1 - Complex Numbers SWBAT: simplify negative radicals using imaginary numbers, 2) simplify powers if i, and 3) graph complex numbers. Warm - Up:

Chapter 5: Complex Numbers · 4 Day 1 - Complex Numbers SWBAT: simplify negative radicals using imaginary numbers, 2) simplify powers if i, and 3) graph complex numbers. Warm - Up:

Documents

Imaginary & Complex Numbers. Once upon a time… -In the set of real numbers, negative numbers do not have square roots. -Imaginary numbers were invented

Imaginary & Complex Numbers. Once upon a time… -In the set of real numbers, negative numbers do not have square roots. -Imaginary numbers were invented

Documents

Review on imaginary and complex numbers

Review on imaginary and complex numbers

Documents

Complex Variables. Complex numbers are really two numbers packaged into one entity (much like matrices). The two numbers are the real and imaginary portions

Complex Variables. Complex numbers are really two numbers packaged into one entity (much like matrices). The two numbers are the real and imaginary portions

Documents

Complex Numbers 10.7 1.Write imaginary numbers using i. 2.Perform arithmetic operations with complex numbers. 3.Raise i to powers

Complex Numbers 10.7 1.Write imaginary numbers using i. 2.Perform arithmetic operations with complex numbers. 3.Raise i to powers

Documents

Holt Algebra 2 5-5 Complex Numbers and Roots Define and use imaginary and complex numbers. Solve quadratic equations with complex roots. Objectives

Holt Algebra 2 5-5 Complex Numbers and Roots Define and use imaginary and complex numbers. Solve quadratic equations with complex roots. Objectives

Documents

1 Simplify Problems With Imaginary Roots Standards 5 & 6 Equation That Results In Imaginary Roots COMPLEX NUMBERS Complex Numbers In Context END SHOW Imaginary

1 Simplify Problems With Imaginary Roots Standards 5 & 6 Equation That Results In Imaginary Roots COMPLEX NUMBERS Complex Numbers In Context END SHOW Imaginary

Documents

2.4 Complex Numbers Students will use the imaginary unit i to write complex numbers. Students will add, subtract, and multiply complex numbers. Students

2.4 Complex Numbers Students will use the imaginary unit i to write complex numbers. Students will add, subtract, and multiply complex numbers. Students

Documents

Use the imaginary unit i to write complex numbers. Add, subtract, and multiply complex numbers

Use the imaginary unit i to write complex numbers. Add, subtract, and multiply complex numbers

Documents

Section 1.4 Complex Numbers. The Imaginary Unit i

Section 1.4 Complex Numbers. The Imaginary Unit i

Documents

COMPLEX NUMBERS Unit 4Radicals. Complex/Imaginary Numbers WHAT IS? WHY? There is no real number whose square is -25 so we have to use an imaginary number

COMPLEX NUMBERS Unit 4Radicals. Complex/Imaginary Numbers WHAT IS? WHY? There is no real number whose square is -25 so we have to use an imaginary number

Documents

4.8 Complex Numbers Ch 4...Algebra 2 Notes, Chapter 4 1 4.8 Complex Numbers A. Imaginary Numbers Consider: 25 2 Has no REAL solution because (?) = -25 Imaginary Numbers were created

4.8 Complex Numbers Ch 4...Algebra 2 Notes, Chapter 4 1 4.8 Complex Numbers A. Imaginary Numbers Consider: 25 2 Has no REAL solution because (?) = -25 Imaginary Numbers were created

Documents

Introduction to Simplifying Radicals radicals... · · 2017-12-12Junior Radicals/Imaginary/Complex Numbers Packet #4 3 7 ... Junior Radicals/Imaginary/Complex Numbers Packet #4

Introduction to Simplifying Radicals radicals... · · 2017-12-12Junior Radicals/Imaginary/Complex Numbers Packet #4 3 7 ... Junior Radicals/Imaginary/Complex Numbers Packet #4

Documents

Sec 1.4 –Revisiting Quadratics The Imaginary Number and Complex Numbers … · 2019. 3. 28. · Sec 1.4 –Revisiting Quadratics The Imaginary Number and Complex Numbers Name: For

Sec 1.4 –Revisiting Quadratics The Imaginary Number and Complex Numbers … · 2019. 3. 28. · Sec 1.4 –Revisiting Quadratics The Imaginary Number and Complex Numbers Name: For

Documents

Appendix E Complex Numbers E1 E Complex Numberss17.middlebury.edu/MATH0225A/Complex Numbers.pdf · To add (or subtract) two complex numbers, you add (or subtract) the real and imaginary

Appendix E Complex Numbers E1 E Complex Numberss17.middlebury.edu/MATH0225A/Complex Numbers.pdf · To add (or subtract) two complex numbers, you add (or subtract) the real and imaginary

Documents

Complex numbers i or j. Complex numbers An Imaginary Number, when squared, gives a negative result. imaginary 2 = negative

Complex numbers i or j. Complex numbers An Imaginary Number, when squared, gives a negative result. imaginary 2 = negative

Documents

5.4 – Complex Numbers Our Imaginary Friends Uses of Imaginary Numbers Contrary to its name, the “imaginary number” exists in a similar fashion to the

5.4 – Complex Numbers Our Imaginary Friends Uses of Imaginary Numbers Contrary to its name, the “imaginary number” exists in a similar fashion to the

Documents

5.9: Imaginary + Complex Numbers -Defining i -Simplifying negative radicands -Powers of i -Solving equations -Complex numbers -Operations with complex

5.9: Imaginary + Complex Numbers -Defining i -Simplifying negative radicands -Powers of i -Solving equations -Complex numbers -Operations with complex

Documents

4.1.1 Real Numbers - courses.modernstates.org · 4.2.1 Complex Numbers • Complex numbers extend the real numbers by introducing the imaginary unit . • A complex number is of the

4.1.1 Real Numbers - courses.modernstates.org · 4.2.1 Complex Numbers • Complex numbers extend the real numbers by introducing the imaginary unit . • A complex number is of the

Documents

Use the imaginary unit i to write complex numbers. Add, subtract, and multiply complex numbers. Use complex conjugates to write the quotient of two

Use the imaginary unit i to write complex numbers. Add, subtract, and multiply complex numbers. Use complex conjugates to write the quotient of two

Documents

Complex Numbers? What’s So Complex?. Complex numbers are vectors represented in the complex plane as the sum of a Real part and an Imaginary part: z =

Complex Numbers? What’s So Complex?. Complex numbers are vectors represented in the complex plane as the sum of a Real part and an Imaginary part: z =

Documents

8 Complex Vector Spaces - Cengage€¦ · 392 Chapter 8 Complex Vector Spaces 8.1 Complex Numbers Use the imaginary unit to write complex numbers. Graphically represent …

8 Complex Vector Spaces - Cengage€¦ · 392 Chapter 8 Complex Vector Spaces 8.1 Complex Numbers Use the imaginary unit to write complex numbers. Graphically represent …

Documents