One of the few certainties in LC Maths is Complex Numbers appearing as a Part A (25 Mark) question.
This post gives 5 Tips to consider when revising Complex Numbers.
The interesting thing about Complex Numbers is HOW they come up each year in the LCHL exam. Keep a look out for Tip No. 5 which lists exactly this from the last few years.
FREE SAMPLE: Leaving Cert 2016-17
In Leaving Cert 2016 and 2017 threw up two challenging Complex Numbers questions.
Scroll down to the bottom to find FREE ACCESS to:
- The Worksheet
- The Powerpoint Solutions (FAO Teachers!)
Algebra/Factor Theorem V De Moivre's Theorem
It might be good to keep in mind, the Complex Number topic can be split in two.
Often in Maths, identifying what type of question being asked can be half the battle.
With Complex Numbers, the first step should be identifying is it Algebra or the Factor Theorem, or is it a Polar Form/De Moivre's Theorem question,
2. Speaking of the Algebra and the Factor Theorem...
Worksheet: Page 4 - 5
Powerpoint: Page 8 - 11
It should be immediately obvious when first learning Complex Numbers that many of the concepts involved have been covered before.
For example: Algebra Identities, Roots of a Quadratic/Cubic function, Algebra Fractions.
Before you start revising Complex Numbers it is highly recommended to go back over these concepts first (see worksheet).
3. Revise Trigonometric Functions
Worksheet: Page 8
Powerpoint: Page 23- 26
Radians, Sine Functions, Unit Circle, General Solutions... These concepts often strike fear in LCHL students. But they are fundamental not only to the Trigonometry chapter, but also to getting a full understanding of De Moivre's Theorem.
It might be a good idea to go back over this before tackling Complex Numbers
4. Solving Complex Equations
Worksheet: Page 13 - 14
Powerpoint: Page 46 - 51
Arguably the most challenging of Complex Numbers is solving Complex Equations (see image above). It incorporates everything you would have learned for De Moivre's theorem.
Good News: The good thing about these type of questions is they are quite routine. They do not change much when they come up. This example in the image came up in LC 2022.
5. Exam Questions - Different Types
Very often, Complex Numbers questions can be quite predictable. They can come up simply with Algebra, Factor Theorem and De Moivre's Theorem.
However, one of the aims of the Leaving Cert is for students to make connections across different topics. This is often the case with Complex Numbers.
Here is a list of the topics that Complex Numbers has been combined with over the last 7 years of the Leaving Cert:
LC 2022: With the Circle
LC 2021: With Surds
LC 2020: With Sequences & Series
LC 2019: With the Factor Theorem
LC 2018: With Proof by Induction
LC 2017: With Trigonometry/Geometry
LC 2016: With the Factor Theorem
LC 2015: With Sequences & Series
Leaving Cert 2016 - 17: Paper 1 Question
BEFORE you look for the solutions below, why not try out these two questions yourself first!
Save time and effort with the POWERPOINT solutions of these two exam questions.
Would you have approached these differently?
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