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5. Complex numbers

#### Investigation: The Continuity Principle can surprise us.

A Mathematical Investigation Assessment Item for Yr 10 Ext. - Yr 11 Mathematics Specialists (in WA MAS Units 1&amp;2). Enjoy the surprise!

#### 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.

#### 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…

#### 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!

#### 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.

#### 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.*

#### Complex Numbers Notes and Activities

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

#### 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!

#### Euler's prime number Generator and 163

Presentation showing the solution of Euler's quadratic formula for generating primes and noting its irrational imaginary part of its complex solutions. When Euler's number, e is then taken to the power of pi*square root of 163 one mysteriously ends up with almost an integer-shown in wolfram. Link then to numberphile video that takes a different broader angle.

#### Mathematical Ambiguity & topic relationships

A presentation exploring ambiguity in the operations and objects of Maths and a set of concept maps that connect various topics of GCSE and IB/A level syllabuses. Quadratic, Log, Trigonometric and Functions are mapped in detail. Useful crossover introductory material that can provide some meaning and context in helping to make some connections between otherwise disparate fields. The presentation develops five areas in which the terms and processes of mathematics are inherently ambiguous: from the irrationals and infinity, the variable as a receptacle, the filling of the number line, forming operations with numbers to the notion of equality and sameness. That is from a number being both a noun (a fractional object) and a verb (process of adding a convergent series of rationals). That algebraic formulations using a variable x, allow for x in one sense to have any value ( before the equation is solved) to a specific value when it has been solved. As five separate chapters each one can serve as nonstandard provocative discussion/starter/plenary material .

#### Composite functions + complex numbers

The topics in this resource covers the requirements of the new GCSE Mathematics syllabus and provides an easy to follow explanation of the topics of composite functions and complex numbers. The resource is suitable for the higher GCSE pupils.

#### Advanced Higher Maths Complete Course Resource Bundle

Advanced Higher Maths Complete Course Resource Bundle

#### Conjugate root theorem, sum and product of polynomial roots

Power Point presentation, 12 slides, demonstrating that for a given polynomial that has a complex zero z, then its conjugate z* is also a zero of the polynomial, based on IB Higher level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OldENnRERSZ29PYU0/view?usp=sharing

#### Solving system of equations

Power Point presentation, 10 slides, Explaining how to solve system of equations with two or three unknowns, using the methods of substitutions, elimination and the Gaussian elimination Method, based on IB Higher level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlcW9QalZzSm9JX2s/view?usp=sharing

#### Complex numbers - PowerPoint

Complex numbers - introduction, imaginary number i, addition, subtraction, multiplication and division of complex numbers.

#### complex numbers solved problems

complex numbers solved problems for high schools students contain some good ideas

#### Past paper questions on Complex Numbers

Past paper questions on complex numbers with marking scheme of Cambridge A level Pure Maths 3 (9709)

#### OCR FP1 Complex Number Practise

This is a collection of revision questions for OCR FP1 adapted from AQA papers FP1 and FP2. It covers mainly solving equations and loci as these are the sections my students tend to struggle on.

#### Method for Multiplying Complex Numbers

This is a worksheet for students to practice using the box method for multiplying complex numbers. It includes a clear example at the top as well as three exercises with blank boxes already provided for students to fill.

#### Complex Numbers Selection

Complex Numbers Selection

#### Surds - GCSE Maths - Number (suitable for 9 - 1 specification)

Complete lessons covering all of the requirements within the Surds. Visit weteachmaths.co.uk for - Lessons and worksheets suitable for the 9 - 1 GCSE Specification - A-Level teaching resources for Core 1, Core 2, Core 3, Core 4, Decision 1 and Statistics 1 - Teaching resources for Level 3 Core Mathematics - Schemes of work for Higher and Foundation GCSE Maths (adapted for the 9 - 1 specification) - Topic tests for GCSE Maths and A-Level Maths - Support for the teaching and coursework in GCSE Statistics

#### Treasure Hunts for Matrices topic

This pack consists of two treasure hunts and two true/false trails relating to matrix arithmetic and transformations. There is a standard and more challenging version of each activity.

#### Graphing equations by plotting points - part 2

This video shows how to graph equations by plotting points. Part 2 of 2 http://www.mathispower4u.yolasite.com

#### Graphing equations by plotting points - part 1

This video shows how to graph equations by plotting points. Part 1 of 2 http://www.mathispower4u.yolasite.com

#### Compounded interest

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#### Perpendicular bisector of a segment on the coordinate plane

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#### The medians of a triangle

This video introduces the medians of a triangle and states the properties of the medians of a triangle. Complete Video List: http://mathispower4u.yolasite.com/

#### Examples: using the properties of the medians of a triangle to solve for unknown values

This video provided example problems of using the properties of the medians of a triangle to solve for unknown values. Complete Video List: http://mathispower4u.yolasite.com/

#### Introduction to the midsegments of a triangle

This video introduces midsegments of a triangle and states the properties of the midsegments of a triangle. Complete Video List: http://mathispower4u.yolasite.com/

#### Examples: determining unknown values using properties of the midsegments of a triangle

This video provided example problems of how to determine unknown values using the properties of the midsegments of a triangle. Complete Video List: http://mathispower4u.yolasite.com/

#### Proof: the angle bisector theorem

This video states and proves the angle bisector theorem. Complete Video List: http://www.mathispower4u.yolasite.com

#### Proof: perpendicular bisector theorem

This videos states and proves the perpendicular bisector theorem. Complete Video List: http://www.mathispower4u.yolasite.com

#### Proof: the angle bisector theorem converse

This video states and proves the angle bisector theorem converse. Complete Video List: http://www.mathispower4u.yolasite.com

#### Proof: the angle of a triangle opposite the longest side is the largest angle

This video proves if the one side of a triangle is longer than another, then the angle opposite the longer side is greater than the angle opposite the shorter side. Complete Video List: http://www.mathispower4u.yolasite.com

#### Proof: perpendicular bisector theorem converse

This videos states and proves the perpendicular bisector theorem converse. Complete Video List: http://www.mathispower4u.yolasite.com

#### Using the properties of the triangle angle bisector theorem to determine unknown values

Complete Video List: http://www.mathispower4u.yolasite.com

#### Tangent lines to a circle

This video will state and prove the Tangent to a Circle Theorem. Complete Video List: http://www.mathispower4u.yolasite.com

#### Prove tangent segments to a circle from a point are congruent

This video proves tangent segments to a circle from a single point are congruent. Complete Video List: http://www.mathispower4u.yolasite.com