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#### The Complex Number System

These notes and examples cover the US Common Core N-CN standards for complex numbers. The student booklet has spaces to fill in the solutions to the examples. The separate teacher booklet has detailed worked solutions. The student booklet is provided in both docx and pdf forms so that it can be edited to suit the needs of your class.

#### IB Maths HL - Complete Notes + Calculus Option

Complete notes including notes on Topic 9, the Calculus Option This is a collection of all of the notes I have written for my IB Maths HL class. They are handwritten, concise notes, covering the whole course in 100 pages. Topic 1 - Algebra - 21 Pages Topic 2 - Functions - 10 Pages Topic 3 - Trigonometry - 6 Pages Topic 4 - Vectors - 10 Pages Topic 5 - Statistics &amp; Probability - 10 Pages Topic 6 - Calculus - 20 Pages Topic 9 - Calculus Option - 23 Pages If you would like to see what you would be getting, you can download Topic 1 of IB SL or IB Math Studies for free. I hope you enjoy, and please ‘follow’, as I will be uploading other IB resources soon.

#### AQA Further Pure 1 Jan 2013 Model Solutions

Model solutions for the AQA further maths Further Pure Jan 2013 paper with comments and notes. Great for peer marking after completing the paper to see what their answers should look like. Very clear and concise.

#### OCR MEI FP2 & S2 Full SOW + D1&S1 Revision

75% saving! Two resource packs that contain all the PowerPoints required to teach the full modules for FP2 and S2 for MEI OCR. Revision PowerPoints are also contained in these resource packs. I have also included D1 revision questions which can be used for the new maths A Level. I have also included Statistics revision worksheets which can be adapted for the new maths A Level.

#### MEI FP2 SOW

15 PowerPoints that covers every topic for MEI FP2. Revision PowerPoints are also included to revise Hyperbolics, Polar Coordinates and MacLaurin Series

#### FP2 Notes and Examples

You will receive a student booklet with gaps for the solutions to the examples to be filled in and a teacher’s booklet with detailed worked solutions.

#### FP1 Notes and Examples

You will receive a student booklet with gaps for the solutions to the examples to be filled in and a teacher’s booklet with detailed worked solutions.

#### IB Maths HL - Complete Notes

Complete notes, without any option topics, just the main topics 1 to 6 This is a collection of all of the notes I have written for my IB Maths HL class. They are handwritten, concise notes, covering the whole course in 77 pages. Topic 1 - Algebra - 21 Pages Topic 2 - Functions - 10 Pages Topic 3 - Trigonometry - 6 Pages Topic 4 - Vectors - 10 Pages Topic 5 - Statistics &amp; Probability - 10 Pages Topic 6 - Calculus - 20 Pages If you would like to see what you would be getting, you can download Topic 1 of IB SL or IB Math Studies for free. I hope you enjoy, and please ‘follow’, as I will be uploading other IB resources soon.

#### Edexcel Further Core Pure AS

These notes and examples contain everything you need to deliver the new Edexcel Further Core Pure AS content. There are 6 student booklets and 6 teacher booklets containing detailed solutions to all examples.

#### Edexcel Further Core Pure AS Topic 2: Further Algebra

These notes and examples are designed for the delivery of the new Edexcel A Level Further Maths Linear Specification. You will receive an editable Word document that can be issued to students with gaps for them to fill in the solutions to the examples and make further notes. Full solutions to the examples are provided for the teacher in the form of a PDF document. This could be made available to students if they miss a lesson, reducing teacher workload. Each topic is available as a separate purchase, or you can download the entire set covering all the the Core Pure AS content. To purchase the complete set of notes for the Core Pure AS content, click here: [https://www.tes.com/teaching-resource/edexcel-further-core-pure-as-11890483]

#### Edexcel Further Core Pure AS Topic 1: Complex Numbers

These notes and examples are designed for the delivery of the new Edexcel A Level Further Maths Linear Specification. You will receive an editable Word document that can be issued to students with gaps for them to fill in the solutions to the examples and make further notes. Full solutions to the examples are provided for the teacher in the form of a PDF document. This could be made available to students if they miss a lesson, reducing teacher workload. Each topic is available as a separate purchase, or you can download the entire set covering all the the Core Pure AS content. To purchase the complete set of notes for the Core Pure AS content, click here: [https://www.tes.com/teaching-resource/edexcel-further-core-pure-as-11890483]

#### Eulers identity fun year 10 lesson

A fun end of term lesson I used with my top set year 10s (after they bugged me to teach them about complex numbers for eons). I wouldn’t necessarily suggest this for anyone other than very capable, extremely engaged mathematicians…

#### Operations with Complex Numbers Color by Number

With this activity, students will simplify complex number expressions and then color the picture according to the directions and color indicated to reveal a beautiful, colorful mandala! As an added bonus, the final products make fabulous classroom decor! This activity is an excellent resource for sub plans, enrichment/reinforcement, early finishers, and extra practice with some fun. It is especially useful for end-of-year practice, spiral review, and motivated practice when students are exhausted from standardized testing or mentally “checked out” before a long break (hello summer!). Teachers and students alike enjoy motivating activities, so engage your students today with these fun coloring activities!

#### Absolute Value of Complex Numbers Color by Number

With this activity, students will find the absolute value of complex numbers and then color the picture according to the color indicated to reveal a beautiful, colorful mandala! As an added bonus, the final products make fabulous classroom decor! This activity is an excellent resource for sub plans, enrichment/reinforcement, early finishers, and extra practice with some fun. It is especially useful for end-of-year practice, spiral review, and motivated practice when students are exhausted from standardized testing or mentally “checked out” before a long break (hello summer!). Teachers and students alike enjoy motivating activities, so engage your students today with these fun coloring activities!

#### Set Theory PowerPoint and Handouts

An extensive introduction to Set Theory, generally aimed at Computer Science A Level students, A Level Mathematicians or first year Undergraduate students in either Computer Science or Mathematics. It is intended to cover two lessons, extra examples and discussion may be required if aiming at a lower ability. Includes: A simple starter to encourage discussion on how to categorise numbers, as well as how many there may be e.g. how many natural numbers are there? A handout featuring all definitions given in the PowerPoint A PowerPoint covering set notation, intersections, unions, set comprehension and set compression. More resources can be added upon request. Please do give feedback/suggestions!

#### Complex Numbers

A complete unit of work for Complex numbers: Cartesian form, modulus-argument firm, Euler’s form, de Moivre’s theorem, nth roots of a complex number, fundamental theorem of algebra, conjugate root theorem, solving polynomial equations over C, regions in a complex plane. Class activities, notes, power point presentations, assessment. Using TI Nspire CAS.

#### Binomial Theorem, Partial Fractions, Complex Numbers

Three homeworks and a set of extended questions on the topics of Expansions with the Binomial Theorem Using Partial Fractions Complex Numbers, operations, polynomials, Argand diagrams and De Moivres Theorem All provided with comprehensive solutions

#### FP1

FP1 Module formula and revision notes.

#### Multiplying Complex Numbers – Math puzzle

Multiplying Complex Numbers – Math puzzle Use conjugates to rationalize a denominator. I’ve included three different sizes of the same puzzle. The smaller size is only two pages and is great if you are going to print of individual (or to work in pairs) copies for students to practice in class or at home. The larger size requires 3 pieces of paper and quite a bit of space to solve – fun for centers and group work. The extra-large size requires 8 pieces of paper. Cut out the puzzle pieces (or even better if your students do it themselves) and students are to solve the puzzle so that it matches the solution provided. If your students are going to cut out the pieces then no prep is needed – the puzzle is not in order. I’ve been using these puzzles for years with great success! I recommend printing the puzzles on colourful paper and laminating them. This way you only have to cut them out once and they will last for years! What is included in this product? • The solution to the puzzle – Page 3 • The normal size puzzle – Pages 4 – 5 • The large size puzzle – Pages 6 – 8 • The extra-large size puzzle – Pages 9 – 16 • Questions and Answers in a table format for easy grading or you can cut these out to play a matching game – Pages 17 – 19 My students love doing these types of puzzles. This product can also be used as a perfect revision of the school work to do at home. All answers can be easily checked thanks to the included solution to the puzzle or questions and answers shown in a table. Thank you for checking my resources.

#### MathDBase Desktop Math Reference

Subjects: Algebra, Geometry, Trigonometry Grade Levels: 7th, 8th, 9th, 10th, 11th, 12th, Higher Education, Adult Education, Homeschool Resource Type: E-books A handy reference with useful math facts from Arithmetic, Algebra, Geometry and Trigonometry. Revised version with additional Binomial Expansion information. Note: Trying to download and open this e-book on a phone usually causes a problem...there is no password required.

#### Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2012"

A Further Maths &quot;past paper&quot; for Pure Core 1 on the new syllabus on Edexcel (2017). This is a &quot;past paper&quot; that takes questions from the June 2012 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.

#### 40 slide Powerpoint Advanced Higher Maths Complex Numbers Argand Diagrams Worked Solutions

40 slide Powerpoint for Advanced Higher Maths Unit 2: Complex Numbers. There is a brief revision of the basics of Complex numbers followed by a series of questions. The 24 questions (many of them multi-part) require the construction of Argand Diagrams, use of the quadratic formula, polynomial long division, and simultaneous equations. There are fully worked solutions (including diagrams) for complex number topics relating to: Equating Real and Imaginary Parts; Finding square, cube, fourth, fifth and sixth roots of complex numbers (including unity) and plotting them on an Argand diagram; Verifying and finding roots of complex number polynomials; Expanding and simplifying complex numbers using the Binomial Theorem and De Moivre’s Theorem; Interpreting geometrically loci in the complex plane; Conversions between polar and rectangular forms; Complex Conjugates; Exponential Form; Trigonometric identities, substitutions and simplification. The questions are grouped in approximate order of difficulty and to match the usual order of progress through this topic. *Animated workings come up line by line on mouse clicks.*

#### Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2013"

A Further Maths &quot;past paper&quot; for Pure Core 1 on the new syllabus on Edexcel (2017). This is a &quot;past paper&quot; that takes questions from the June 2013 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.

#### Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2014"

A Further Maths &quot;past paper&quot; for Pure Core 1 on the new syllabus on Edexcel (2017). This is a &quot;past paper&quot; that takes questions from the June 2014 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.

#### Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2015"

A Further Maths &quot;past paper&quot; for Pure Core 1 on the new syllabus on Edexcel (2017). This is a &quot;past paper&quot; that takes questions from the June 2015 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.

#### Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2016"

A Further Maths &quot;past paper&quot; for Pure Core 1 on the new syllabus on Edexcel (2017). This is a &quot;past paper&quot; that takes questions from the June 2016 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.

#### Complex numbers - polar form, calculations and geometrical applications

The first resource introduces the technique for writing a complex number z=a+bi in (trigonometric) polar form, r(cos (theta)+ i sin(theta)), there are few examples of converting from one form into the other (to do as a class), and then an exercise of 30 questions for students to do. The next section introduces the exponential polar form re^(i theta), a few examples of converting from one form into the other (to do as a class), and then an exercise of questions for students to do. The exercise includes questions that get students to consider what z* and -z look like in both polar forms, as well as investigating multiplying and dividing complex numbers in polar form. Answers to the exercises are included. The second resource begins with a reminder of how to multiply/divide complex numbers in polar form, followed by an exercise of questions to practise. The remaining 3 pages cover the geometrical effect of multiplying, with several examples for students to learn from. Fully worked solutions are included. The final resource focuses on examination-style questions that consider the geometric effect of multiplying by a complex number in polar form. Fully worked solutions are included.

#### Complex numbers

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1, which is called an imaginary number because there is no real number that satisfies this equation. For the complex number a + bi, a is called the real part, and b is called the imaginary part. This lesson is suitable for the AS and A level pupils and is written in a pupil friendly manner in order to help the students easily master the topic and go on to solve all of the relevant questions with ease and confidence.

#### Finding roots and real factors of z^n+k=0

The first resource guides your class through the process of using the real and complex roots of z^n+k=0 to write down its real factors. The introduction includes the important result about the sum of conjugates and then uses equations of the form z^n=1 or z^n=-1 to establish that there is always an even number of complex roots, which can be put into conjugate pairs. It is then shown how each conjugate pair of roots produces a real quadratic factor, while each real root produces a real linear factor. To practise all this there is an exercise with 7 questions for students to complete. Solutions to all the examples and the exercise are included. The second resource contains an exercise with further examination-style questions on this topic. This could be used as additional practice in class or as a homework/test. Answers are provided.

#### IB Maths HL - Topic 1 Algebra - Notes

Handwritten notes that I made for my HL students on Topic 1 of Algebra in the IB. It includes: 1.1 - Sequences &amp; Series 1.2 - Exponents and Logs 1.3 - Binomial Expansion &amp; Permutations/Combinations 1.4 - Proof by Induction 1.5 - Complex Numbers 1.6 - Complex (Polar Form) 1.7 - De Moivre's Theorem/Euler's Theorem 1.8 - Complex Conjugate Roots of Polynomials 1.9 - Solving Systems of Equations with 3 variables If you are an HL teacher (or student) and you found these helpful, please 'follow' me, then you will see as soon as I get around to uploading the remaining topics of the HL course (Feb/March/April 2018).

#### PreCalculus Unit 2 Polynomial Power functions and rational functions Interactive Notebooks Only

This is a complete set of foldables for PreCalculus Unit 2 Quadratic and Rational Functions. Sets include: - Color-coded graphic organizers* - Black-line master graphic organizers - Color coded notes with examples. - Practice problems or activity such as puzzle or card sort, great for homework - Answer key for practice problems Topics include: - Vertex and standard form of quadratic functions - Graphing Quadratic Functions (NEW! Not yet available elsewhere in the store) - Zeros of Polynomial functions (NEW! Not yet available elsewhere in the store) - Polynomial Division Interactive Notebook including long and synthetic division - Complex numbers - Graphing rational functions

#### Complex Numbers Starters and Worksheets

Starters and main worksheets for two lessons' worth on complex numbers.

#### Complex numbers

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit (which satisfies the equation i2 = −1). In this expression, a is called the real part of the complex number, and b is called the imaginary part. This resource is suitable for 'A level,' students studying C1-C2. The lesson carefully explains the topic of complex numbers in an easy to follow manner.

#### Homeworks (Pure) - New AS Further Maths Syllabus

I have included 3 sections as a free sample which you be able to find towards the bottom of this page. Split into 15 sections 1. Complex Numbers 1 2. Complex Numbers 2 3. Conic Sections 4. Hyperbolic Functions 5. Maclaurin’s Series 6. Matrices 1 7. Matrices 2 8. Method of Differences 9. Polar Coordinates 10. Proof by Induction 11. Rational Functions 12. Roots of Polynomials 13. Summation Series 14. Vectors 15. Vol. of Rev. and Mean Value Each section has 4 documents 1. Homework 2. Full worked solutions for homework 3. Challenge Questions for gifted students 4. Full worked solutions for Challenge Questions • Includes both the PDF’s and word documents which are fully editable. • They are written for the AQA syllabus but can be adapted for other exam boards. • The homework’s are intentionally quite difficult and written in an exam style. • Each homework has ~50% of the answers provided, this is to allow students to check they’re getting the first few questions correct. You can remove this if you want. Note: As there is a lot of content here there may be a few typos, I’ll be sure to update any mistakes as soon as I’m aware of them. The questions and solutions should be close to 100% accurate though.

#### Homeworks (Pure) - New AS Further Maths Syllabus

These are 3 free sample sections from my Further Maths Homework collection. You should be able to find the full 15 sections at the bottom of the page.

#### Complex Numbers FP2 Topic Mats

Structured worksheet to help pupils take key notes and examples for the FP2 topic of Complex Numbers. Designed for Edexcel specification.

#### Complex Numbers Notes and Activities

Save with this set of 3 resources for using complex numbers including operations and graphing complex numbers.

#### Argand Diagrams Relay

Works well as a plenary to a double lesson on Argand Diagrams or as part of revision. The template helps to reinforce accuracy and good presentation.

#### Complex Numbers

Everything about Complex Numbers pitched for A level students studying the CIE syllabus including:- Understand the idea of a complex number. Carry out operations on on 2 complex numbers expressed in cartesian form. Understand that polynomials with real coefficient, any non real roots occur in complex conjugate pair. Find the complex roots of quadratic and cubic equations. Find the square roots of a complex number. Convert a complex number to polar form and vice versa. Convert a complex number to exponential form and vice versa. Represent a complex number on an Argand Diagram. Represent complex numbers geometrically.

#### Further Maths for Engineers

Powerpoints that cover the BTEC further maths for engineers unit

#### Trigonometry Polar and Rectangular Coordinates

Algebra 2/Trigonometry: 20 page Polar and Rectangular Coordinates includes brief notes, examples, and practice test (with detailed solutions).. Topics cover converting polar to rectangular; plotting polar coordinates; complex number system, and more; Also, imaginary numbers quiz, and 3 comics. Available at mathplane.org. (Or, download here and support mathplane and TES.). Thanks for visiting!