2023 SQA Higher Maths Solutions Paper 2 (H Mathematics Past Papers Video)
This video gives the full and detailed solutions to the SQA 2023 Higher Mathematics Paper 2 Exam. There are 15 questions.
If you find this video useful please "like" the video and "subscribe" to my channel https://www.youtube.com/user/mistercorzi Thanks
Here are links to other Maths Higher Past Paper solutions:
2022 SQA Higher Maths Solutions (Papers 1 & 2): https://www.youtube.com/playlist?list=PLvA_gXIhzZNUt59dUmw-3HPjGxZCeO1Nt
2019 SQA Higher Maths Solutions (Papers 1 and 2): https://www.youtube.com/playlist?list=PLvA_gXIhzZNVnEIg55c7pS5NwbLXvfYpb
2018 SQA Higher Maths Paper 1 Solutions: https://www.youtube.com/playlist?list=PLvA_gXIhzZNVPhFvHneRFdG3aZNDV9f3u
2018 SQA Higher Maths Paper 2 Solutions: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWSGBn6WaSqCyh3xZNOJpH7
2017 SQA Higher Maths Paper 1 Solutions: https://www.youtube.com/playlist?list=PLvA_gXIhzZNUWVKDxETEVcNF0YiztsJ3r
2017 SQA Higher Maths Paper 2 Solutions: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWJUN895L3hPW5L5BVgPbrx
2016 SQA CfE Higher Maths Paper 1 Solutions: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWDuEKchmEQqU3Lml022-0a
2016 SQA CfE Higher Maths Paper 2 Solutions: https://www.youtube.com/playlist?list=PLvA_gXIhzZNXKrT1PzQK5SNCxvJEQh9_d
2015 SQA CfE Higher Maths Paper 1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWqmQBV0T2qzvIDd_osAhbL
2015 SQA CfE Higher Maths Paper 2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWM0JAtMbuOReSEQ-j_h7dF
Specimen Paper SQA CfE Higher Maths Paper1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNUwi548Zids_rlRRFcG1Nc0
Specimen Paper SQA CfE Higher Maths Paper 2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNXkHQuKu7BvljcDB2ZgloWS
Chapters
00:00:00 Intro
00:00:38 Question 1a
00:08:03 Question 1b
00:11:51 Question 2
00:16:54 Question 3
00:19:57 Question 4
00:24:47 Question 5
00:28:27 Question 6
00:33:24 Question 7
00:44:18 Question 8
00:53:22 Question 9a
01:06:40 Question 9b
01:11:58 Question 10
01:18:24 Question 11a
01:25:16 Question 11b
01:29:56 Question 12
01:34:35 Question 13a
01:37:41 Question 13b
01:43:22 Question 14a
01:50:45 Question 14b
01:57:10 Question 15
02:05:00 End Links
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2023 SQA Higher Maths Solutions Paper 1 (H Mathematics Past Papers Video)
This video gives the full and detailed solutions to the SQA 2023 Higher Mathematics Paper 1 Exam. There are 14 questions.
If you find this video useful please "like" the video and "subscribe" to my channel https://www.youtube.com/user/mistercorzi Thanks
Here are links to other Maths Higher Past Paper solutions:
2022 SQA Higher Maths Solutions (Papers 1 & 2): https://www.youtube.com/playlist?list=PLvA_gXIhzZNUt59dUmw-3HPjGxZCeO1Nt
2019 SQA Higher Maths Solutions (Papers 1 and 2): https://www.youtube.com/playlist?list=PLvA_gXIhzZNVnEIg55c7pS5NwbLXvfYpb
2018 SQA Higher Maths Paper 1 Solutions: https://www.youtube.com/playlist?list=PLvA_gXIhzZNVPhFvHneRFdG3aZNDV9f3u
2018 SQA Higher Maths Paper 2 Solutions: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWSGBn6WaSqCyh3xZNOJpH7
2017 SQA Higher Maths Paper 1 Solutions: https://www.youtube.com/playlist?list=PLvA_gXIhzZNUWVKDxETEVcNF0YiztsJ3r
2017 SQA Higher Maths Paper 2 Solutions: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWJUN895L3hPW5L5BVgPbrx
2016 SQA CfE Higher Maths Paper 1 Solutions: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWDuEKchmEQqU3Lml022-0a
2016 SQA CfE Higher Maths Paper 2 Solutions: https://www.youtube.com/playlist?list=PLvA_gXIhzZNXKrT1PzQK5SNCxvJEQh9_d
2015 SQA CfE Higher Maths Paper 1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWqmQBV0T2qzvIDd_osAhbL
2015 SQA CfE Higher Maths Paper 2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWM0JAtMbuOReSEQ-j_h7dF
Specimen Paper SQA CfE Higher Maths Paper1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNUwi548Zids_rlRRFcG1Nc0
Specimen Paper SQA CfE Higher Maths Paper 2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNXkHQuKu7BvljcDB2ZgloWS
Chapters
00:00:00 Intro
00:00:39 Question 1
00:04:31 Question 2
00:12:54 Question 3
00:16:12 Question 4a
00:18:45 Question 4b
00:22:27 Question 5
00:29:31 Question 6
00:33:11 Question 7a
00:35:47 Question 7b
00:38:35 Question 8
00:47:35 Question 9
00:53:19 Question 10a
00:56:16 Question 10b
01:01:55 Question 11a
01:06:29 Question 11b
01:09:16 Question 12
01:12:43 Question 13a
01:15:32 Question 13b
01:20:49 End Links
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2023 SQA National 5 Maths Solutions Paper 2 (Nat5 N5 Mathematics Past Papers Video)
This video gives the full and detailed solutions to the SQA 2023 National 5 Mathematics Paper 2 Exam. There are 15 questions.
If you find this video useful please "like" the video and "subscribe" to my channel https://www.youtube.com/user/mistercorzi Thanks
Here are links to other Maths National 5 Past Paper solutions:
2023 N5 Paper 1: https://youtu.be/-Sc28cK0Dx0
2022 N5 Paper 1: https://youtu.be/Vmscd0BbI90
2022 N5 Paper 2: https://youtu.be/15RWqPVPgYk
2019 N5 Paper1 & 2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNXewBSLjKURAIO9R5lF4BDv
2018 N5 Paper 1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNVNDQgWhoyoHA_RoW4UT5Rw
2018 N5 Paper2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNVBatkHAE2ODvuWDzlOlUo9
2017 N5 Paper1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNXeyCndNMKz6kz5CksOn_s0
2017 N5 Paper2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNV_-0LLiVJGqvGNbkBJu01j
2016 N5 Paper1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNVko28iBBdeV0aflHRzyiaD
2016 N5 Paper2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWnCN2c4zLQ_8ps_QmgUQ_k
2015 N5 Paper1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNUTVmdiMMlPElLMVmpOorbo
2015 N5 Paper2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWrwLladBEAyr5I2jVjLY86
2014 N5 Paper1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNVpHM6lonjmy1JXCln35bQT
2014 N5 Paper2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNUM0BNZW9G4ATlpo39e2I7V
Specimen Paper N5 Paper1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNXt8FOLZFHhM1J48rCTeZW4
Specimen Paper N5 Paper2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNV1qWfJLGCu3ntLkMzRvc0J
Chapters
00:00:00 Intro
00:00:40 Question 1
00:05:19 Question 2
00:10:26 Question 3
00:15:13 Question 4
00:21:46 Question 5
00:24:52 Question 6
00:30:04 Question 7
00:33:21 Question 8
00:36:20 Question 9
00:40:46 Question 10
00:44:33 Question 11
00:53:14 Question 12
00:58:34 Question 13
01:01:13 Question 14a
01:03:21 Question 14b
01:09:00 Question 15
01:14:24 End Links
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2023 SQA National 5 Maths Solutions Paper 1 (Nat5 N5 Mathematics Past Papers Video)
This video gives the full and detailed solutions to the SQA 2023 National 5 Mathematics Paper 1 Exam. There are 14 questions.
If you find this video useful please "like" the video and "subscribe" to my channel https://www.youtube.com/user/mistercorzi Thanks
Chapters
00:00:00 Intro
00:00:40 Question 1
00:05:04 Question 2
00:08:10 Question 3
00:15:28 Question 4
00:21:18 Question 5
00:26:50 Question 6
00:32:02 Question 7a
00:42:10 Question 7b
00:43:56 Question 8
00:48:20 Question 9a
00:54:03 Question 9b
00:57:39 Question 10
01:03:20 Question 11
01:13:21 Question 12
01:16:08 Question 13
01:23:26 Question 14
01:28:28 End Links
Here are links to other Maths National 5 Past Paper solutions:
2022 N5 Paper 1: https://youtu.be/Vmscd0BbI90
2022 N5 Paper 2: https://youtu.be/15RWqPVPgYk
2019 N5 Paper1 & 2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNXewBSLjKURAIO9R5lF4BDv
2018 N5 Paper 1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNVNDQgWhoyoHA_RoW4UT5Rw
2018 N5 Paper2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNVBatkHAE2ODvuWDzlOlUo9
2017 N5 Paper1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNXeyCndNMKz6kz5CksOn_s0
2017 N5 Paper2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNV_-0LLiVJGqvGNbkBJu01j
2016 N5 Paper1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNVko28iBBdeV0aflHRzyiaD
2016 N5 Paper2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWnCN2c4zLQ_8ps_QmgUQ_k
2015 N5 Paper1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNUTVmdiMMlPElLMVmpOorbo
2015 N5 Paper2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNWrwLladBEAyr5I2jVjLY86
2014 N5 Paper1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNVpHM6lonjmy1JXCln35bQT
2014 N5 Paper2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNUM0BNZW9G4ATlpo39e2I7V
Specimen Paper N5 Paper1: https://www.youtube.com/playlist?list=PLvA_gXIhzZNXt8FOLZFHhM1J48rCTeZW4
Specimen Paper N5 Paper2: https://www.youtube.com/playlist?list=PLvA_gXIhzZNV1qWfJLGCu3ntLkMzRvc0J
Chiral Aperiodic Monotiles - Their discovery and their construction using Inkscape - Spectre tiles
Hot on the heels of their discovery of the Einstein tiles (The Hat and the Turtle) the same team of David Smith, Joseph Myers, Craig Kaplan and Chaim Goodman-Strauss have made further discoveries. This video explains these new discoveries. Many ideas are covered: periodic and aperiodic tilings, chiral and non-chiral tilings, weakly chiral and strongly chiral aperiodic monotiles.
The weakly chiral aperiodic monotile that David Smith discovered, the first ever such tile discovered, is constructed in this video using the open-source vector graphics software Inkscape. Step-by-step instructions are given for this construction. This tile is then transformed into an example of a Spectre monotile. These are strongly chiral aperiodic monotiles. A colourful tiling is then started.
Inkscape can be downloaded from inkscape.org
Please like the video if you enjoyed watching and don't forget to subscribe to my channel: @mistercorzi
Chapters
0:00 Intro & The controversy surrounding the Hat tile
2:04 Discussion of Chirality
2:37 Animation showing an infinite set of non-chiral aperiodic monotiles
5:28 David Smith's discovery of a chiral aperiodic monotile
7:41 Constructing Tile (1,1) using Inkscape
15:42 Creating a Spectre tile
20:57 Starting a tiling
22:27 End links
"Correction:" 17:40 Symmetric shapes are OK - my mistake.
Other videos in this series:
Using Inkscape to construct the Penrose Tiles (Part 1: Outline shape of the Kite and Dart) https://youtu.be/ru9MrsHaGAk
Using Inkscape to construct the Penrose Tiles (Part 2: Constructing the edge constraint patterns) https://youtu.be/yeSZfd8eu9U
Using Inkscape to construct the Penrose Tiles (Part 3: Exploring Penrose Tiling (Kites and Darts)) https://youtu.be/2LaM_cTinAs
Using Inkscape to construct the Penrose Tiles (Part 4: Inflating a Penrose Tiling (Kites and Darts)) https://youtu.be/h__oFu2T3Ig
Penrose Tiles Part 5 - Kites, Darts, Inflation, Fibonacci Numbers and the Golden Ratio https://youtu.be/vxgIM2Xaa3E
Beyond the Penrose Tiles Part 6 - The Einstein Tile - How to Construct an Aperiodic Monotile Using Inkscape (The Hat Tile) https://youtu.be/BirP2U5l0j0
Beyond the Penrose Tiles Part 7 - The Einstein Tile Part 2: Exploring tiling techniques using Inkscape (Hat Tile)
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Einstein Tile Part 2: Exploring tiling techniques using Inkscape (Hat Tile / Aperiodic Monotile)
SVG File for Einstein Tile / Arrow: https://mistercorzi.scot/svg/hat-arrow.svg
This video explains a tiling method for the Einstein tile known as the Hat. It uses four Supertiles (Hexagon, Triangle, Parallelogram, Fan or pentagonal Fylfot blade) to create a tiling of supertiles. The underlying Hats force matching constraints on the supertiles. Orientation arrows are used to help guide the correct extension of the tiling.
The Einstein Tile called the Hat was discovered by David Smith (UK) and further researched by Joseph Samuel Myers (UK), Craig S. Kaplan (Canada) and Chaim Goodman-Strauss (US). The preprint paper announcing their discovery and detailing their proof of aperiodic tiling (and non-periodic tiling) was published on the ArXiv site on 20th March 2023. Here is the link to the paper: https://arxiv.org/abs/2303.10798
Please like the video if you enjoyed watching and don't forget to subscribe to my channel: @mistercorzi
Chapters
0:00 Introduction
0:43 Document preparation / Import tile
2:43 Hexagon Supertile construction
5:36 Triangle Supertile construction
6:49 Parallelogram Supertile construction
8:20 Fan Supertile construction
10:44 Placing the Arrow Guides
13:09 Supertiling: the 1st iteration
16:45 Supertiling: the 2nd iteration
19:20 Hints of larger structures
20:13 End links
Other videos in this series are:
Using Inkscape to construct the Penrose Tiles (Part 1: Outline shape of the Kite and Dart) https://youtu.be/ru9MrsHaGAk
Using Inkscape to construct the Penrose Tiles (Part 2: Constructing the edge constraint patterns) https://youtu.be/yeSZfd8eu9U
Using Inkscape to construct the Penrose Tiles (Part 3: Exploring Penrose Tiling (Kites and Darts)) https://youtu.be/2LaM_cTinAs
Using Inkscape to construct the Penrose Tiles (Part 4: Inflating a Penrose Tiling (Kites and Darts)) https://youtu.be/h__oFu2T3Ig
Penrose Tiles Part 5 - Kites, Darts, Inflation, Fibonacci Numbers and the Golden Ratio https://youtu.be/vxgIM2Xaa3E
Beyond the Penrose Tiles Part 6 - Einstein Tile: How to Construct an Aperiodic Monotile Using Inkscape (The Hat Tile) https://youtu.be/BirP2U5l0j0
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Einstein Tile - How to Construct an Aperiodic Monotile Using Inkscape (The Hat Tile)
The Hat Tile or Einstein Tile (aperiodic monotile)
The discovery of an "Einstein Tile" was announced on 20th March 2023. This is a single tile that will completely tile the infinite plane but cannot do so in a periodic manner. Such a tile is called an aperiodic monotile. Previously it was not known if such a tile existed.
The video puts this discovery in context by describing how it develops from the work of Roger Penrose and his discovery in the 1970s of the Dart and Kite - a set of two tiles that had the same property.
The video then shows how the tile can be constructed using Inkscape which is a free open source vector graphics software. You are taken through each step in detail.
The video finishes by showing how you can attempt to create a tiling with the tiles you constructed. This is a fun activity.
Inkscape can be downloaded from inkscape.org
Please like the video if you enjoyed watching and don't forget to subscribe to my channel: @mistercorzi
Chapters
0:00 Intro & Context
1:43 Inkscape preparation
3:38 Constructing the tile
10:14 Creating a set of 5 coloured tiles
12:19 How to start tiling
14:39 End links
Other videos in this series:
Using Inkscape to construct the Penrose Tiles (Part 1: Outline shape of the Kite and Dart) https://youtu.be/ru9MrsHaGAk
Using Inkscape to construct the Penrose Tiles (Part 2: Constructing the edge constraint patterns) https://youtu.be/yeSZfd8eu9U
Using Inkscape to construct the Penrose Tiles (Part 3: Exploring Penrose Tiling (Kites and Darts)) https://youtu.be/2LaM_cTinAs
Using Inkscape to construct the Penrose Tiles (Part 4: Inflating a Penrose Tiling (Kites and Darts)) https://youtu.be/h__oFu2T3Ig
Penrose Tiles Part 5 - Kites, Darts, Inflation, Fibonacci Numbers and the Golden Ratio https://youtu.be/vxgIM2Xaa3E
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2022 SQA Higher Maths Solutions Paper 2 (H Mathematics Past Papers Video)
This video gives the full and detailed solutions to the SQA 2022 Higher Mathematics Paper 2 Exam. There are 10 questions.
If you find this video useful please "like" the video and "subscribe" to my channel @mistercorzi Thanks
Chapters
00:00:00 Intro
00:00:35 Question 1a
00:04:43 Question 1b
00:08:02 Question 1c
00:11:28 Question 2
00:16:56 Question 3a
00:25:23 Question 3b
00:30:50 Question 4a
00:38:44 Question 4b
00:44:51 Question 5a
00:48:21 Question 5b
00:52:37 Question 6
01:01:36 Question 7
01:08:02 Question 8a
01:13:09 Question 8b
01:20:54 Question 9a
01:26:28 Question 9b
01:36:06 Question 10a
01:39:34 Question 10b
01:46:25 End Links
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2022 SQA Higher Maths Solutions Paper 1 (H Mathematics Past Papers Video)
This video gives the full and detailed solutions to the SQA 2022 Higher Mathematics Paper 1 Exam. There are 14 questions.
If you find this video useful please "like" the video and "subscribe" to my channel @mistercorzi Thanks
Chapters
00:00:00 Intro
00:00:36 Question 1
00:06:41 Question 2
00:14:08 Question 3
00:18:03 Question 4
00:22:31 Question 5
00:29:04 Question 6
00:36:02 Question 7a
00:38:38 Question 7b
00:41:29 Question 8
00:48:07 Question 9
00:57:45 Question 10a
01:05:57 Question 10b
01:11:32 Question 11
01:16:07 Question 12
01:21:08 Question 13a
01:28:14 Question 13b
01:33:56 Question 14a
01:38:49 Question 14b
01:43:16 End Links
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2022 SQA National 5 Maths Solutions Paper 2 (Nat5 Mathematics Past Papers Video)
This video gives the full and detailed solutions to the SQA 2022 National 5 Mathematics Paper 2 Exam. There are 14 questions.
If you find this video useful please "like" the video and "subscribe" to my channel @mistercorzi Thanks
Chapters
00:00:00 Intro
00:00:32 Question 1
00:04:49 Question 2
00:10:57 Question 3
00:17:05 Question 4a
00:18:40 Question 4b
00:19:27 Question 4c
00:24:44 Question 5a
00:30:35 Question 5b
00:34:16 Question 6
00:38:26 Question 7
00:44:46 Question 8
00:48:59 Question 9
01:04:07 Question 10
01:14:37 Question 11
01:20:53 Question 12
01:24:52 Question 13
01:29:46 Question 14
01:41:11 End Links
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2022 SQA National 5 Maths Solutions Paper 1 (Nat5 Mathematics Past Papers Video)
This video gives the full and detailed solutions to the SQA 2022 National 5 Mathematics Paper 1 Exam. There are 15 questions.
If you find this video useful please "like" the video and "subscribe" to my channel @mistercorzi Thanks
Chapters
00:00:00 Intro
00:00:34 Question 1
00:04:43 Question 2
00:09:32 Question 3
00:13:58 Question 4
00:20:09 Question 5a
00:23:26 Question 5b
00:30:31 Question 6
00:38:38 Question 7
00:43:34 Question 8a
00:46:08 Question 8b
00:50:51 Question 9
00:54:50 Question 10
00:59:05 Question 11
01:01:55 Question 12
01:07:22 Question 13
01:11:20 Question 14
01:17:40 Question 15a
01:19:03 Question 15b
01:23:27 End Links
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10 Complex Numbers and the Unit Circle
This video introduces the idea of the argument and the polar form for complex numbers that lie on the unit circle in the complex plane. Animations are given of both positive and negative rotations to determine arguments and hence the polar form for i, -1, and -i. The modulus and cartesian form of a complex number are also mentioned. Opportunities are given for the viewer to attempt questions during the video. This is No10 in my Complex Analysis video series
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09 Properties of the Modulus of a Complex Number
This video lists some of the more important properties of the modulus of a complex number. The algebraic proofs of these properties are given.
Key Words: complex numbers, modulus, product, quotient, conjugate, negative, proof, algebraic
Other videos in this series are:
01 What is a Complex Number?
02 Adding, Subtracting and Multiplying Complex Numbers
03 Dividing Complex Numbers
04 Complex Conjugates
05 The Field of Complex Numbers
06 The Complex Plane
07 The Modulus of a Complex Number
08 Distance on the Complex Plane
10 Complex Numbers and the Unit Circle
11 The Polar Form of a Complex Number
12 The Principal Argument of a Complex Number
13 The Geometrical Effects of Multiplying by a Complex Number
14 Multiplication of Complex Numbers in Polar Form
15 The Principal Argument when Multiplying Complex Numbers
16 The Geometrical Effects of Dividing by a Complex Number
17 Division of Complex Numbers in Polar Form
18 Properties of the Reciprocal of a Complex Numbers
19 Conjugates and Reciprocals of Complex Numbers
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08 Distance on the Complex Plane
This video illustrates how the modulus can be used to find the distance between two complex numbers on the complex plane (Argand diagram). Viewers are invited to attempt two examples.
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07 The Modulus of a Complex Number
This video introduces the complex number modulus as an extension of the idea of the modulus of a real number. Some examples are given (for the viewer) and some simple proofs are examined.
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06 The Complex Plane
This video introduces the representation of complex numbers by points (and their position vectors) on the Argand diagram. Illustrations show how complex operations correspond to geometrical transformations.
05 The Field of Complex Numbers
This video explores the various properties of addition and multiplication of complex numbers that allow us to call the algebraic structure (C,+,x) a field.
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04 Complex Conjugates
This video explores in depth some of the properties of conjugate complex numbers. The emphasis is on the algebraic properties and aspects of general proof. The viewer is invited to attempt a variety of examples.
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03 Dividing Complex Numbers
This video explains in detail how to divide two complex numbers. Examples involving reciprocals are used first and then some examples involving the division of two complex numbers are explored.
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02 Adding, Subtracting and Multiplying Complex Numbers
Calculating with complex numbers is an essential skill. This video gives illustrative examples of these operations and asks the viewers to participate in the examples.
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01 What is a Complex Number?
The first of a series of videos introducing complex numbers. It would be ideal for anyone starting the study of complex analysis. Basic ideas are illustrated with examples and the viewer is asked to try examples as reinforcement.
Initial discussion of types of numbers (Natural N, Integers Z, Rational Q and Real R) leads on to the topic of the nature of the roots of a quadratic equation. This leads naturally to a specific example and then to a definition of a complex number. The set C of complex numbers is then introduced.
The Real Part (Re z) and Imaginary Part (Im z) of a complex number are illustrated with an exercise for the viewer followed by detailed solutions.
Complex solutions of more quadratic equations are derived and calculations are made by substitution to show that they do indeed satisfy the equations.
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How to draw a Celtic Cross (8 easy stages)
Learn to draw a Celtic Cross in 8 easy stages. You don't have to be an artist to draw this impressive Celtic knot-work Cross. If you can draw dots, diamonds, bits of circles and straight lines you can easily create this work of art.
A fragment of a Gospel Book, now in the Durham Cathedral library and created in northern Britain in the 7th century, contains the earliest example of true knotted designs in the Celtic manner.
True knotwork began in northern Italy and southern Gaul and spread to Ireland by the 7th century. In modern times, Celtic art is popularly thought of in terms of national identity and therefore specifically Irish, Scottish or Welsh.
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Soma Cube Solution (Easily Remembered)
An easily remembered solution to the Soma Cube puzzle. Symmetry is used as a memory aid and each step is explained on the way to assembling the final 3x3x3 cube. You will manage this solution on your own after a couple of views. Good luck!
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Constructing Magic Squares 2
This video shows how to construct a variety of 5x5 magic squares using a simple construction rule. Methods that were developed in the video "Constructing Magic Squares 1" are extended and generalised. After watching this video you should be able to construct these magic squares easily yourself from memory. Give it a try!
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Constructing Magic Squares 1
This video shows how to construct a 3x3 and several 5x5 magic squares using a simple construction rule. After watching this video you should be able to construct these magic squares easily yourself from memory. Give it a try!
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