Topic 10 - Complex Numbers
We have below bronze, silver, gold and platinum tutorials for our Advanced Higher Maths Complex Numbers topic. Typically as you work through the modules, the difficulty of the skills increase by one step ensuring smooth progression. Simply click on the video to play it and pause it at the relevant points for you to attempt your practice question. Each tutorial has a corresponding worksheet for you to download for additional practice. Make sure you have a pen and paper handy! Be sure to mark your work for every exercise attempted. Good luck!
Essential prior knowledge:-
National 5 Maths; E+F 1.1a
- Rationalising the denominator at gold level.
Contents:-
10.1 - Calculations involving complex numbers
10.2 - Solving equations with complex roots
10.3 - The geometry of complex numbers
10.5 - de Moivre's theorem
10.1: Calculations involving complex numbers
Outcome 1 - Bronze Level
Video 65: Adding and subtracting complex numbers. In this video we learn how to add and subtract complex numbers by gathering like terms.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [125.1 KB]
Outcome 2 - Silver Level
Video 66: Multiplying complex numbers. In this video we learn how to multiply complex numbers by forming and breaking brackets.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [134.2 KB]
Outcome 3 - Gold Level
Video 67: Dividing complex numbers. In this video we learn how to divide complex numbers through some "clever" manipulation involving the complex conjugate.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [133.7 KB]
Outcome 4 - Platinum Level
Video 68: Square rooting complex numbers. In this video we learn how to square root complex numbers by forming and solving an equation.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [148.0 KB]
10.2: Solving equations with complex roots
Outcome 2 - Silver Level
Video 70: Solving cubic equations. In this video we learn how to find the 3rd root in a cubic equation when given the other two.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [144.2 KB]
Outcome 3 - Gold Level
Video 71: Solving quartic equations. In this video we learn how to find the other two roots in a quartic equation when given the first two.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [147.6 KB]
10.3: The geometry of complex numbers
Outcome 1 - Bronze Level
Video 72: The geometry of complex numbers in the first quadrant. In this video we learn how to represent a complex number in the first quadrant of an argand diagram, calculate the modulus and argument and write in polar form.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [148.8 KB]
Outcome 2 - Silver Level
Video 73: The geometry of complex numbers in the second quadrant. In this video we learn how to represent a complex number in the second quadrant of an argand diagram, calculate the modulus and argument and write in polar form.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [152.5 KB]
Outcome 3 - Gold Level
Video 74: The geometry of complex numbers in the fourth quadrant. In this video we learn how to represent a complex number in the fourth quadrant of an argand diagram, calculate the modulus and argument and write in polar form.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [150.7 KB]
Outcome 4 - Platinum Level
Video 75: The geometry of complex numbers in the third quadrant. In this video we learn how to represent a complex number in the third quadrant of an argand diagram, calculate the modulus and argument and write in polar form.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [157.9 KB]
10.5: de Moivre's theorem
Outcome 1 - Bronze Level
Video 76: de Moivre's theorem. In this video we will learn how to multiply complex numbers in polar form which will allow us to evaluate complex numbers raised to a power.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [132.4 KB]
Congratulations
You have completed this module - well done! Remember to go back and redo any areas of weakness, that's how we improve. If you are happy with all areas, go back to the main menu and pick another topic to practice!
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