LCHL Maths – Complex Numbers

Leaving Cert Higher Level Maths LCHL Maths – Complex Numbers

LCHL Complex Numbers

Your progress through this topic0 of 17 lessons

Lessons in this topic

All 17 lessons, in order — each one ticks off as you open it.

1Introduction 2Addition, Subtraction, Multiplication 3Division and Conjugates 4Argand Plane and Modulus 5Modulus and conjugates 6Equating Co-efficients 7Rotations 8Quadratic equations 9Cubic equations 10Introduction to Polar Form 11Rules for Polar Form 12Introduction to De Moivres theorem 13Converting to polar form and applying De Moivres theorem 14Using De Moivres theorem to find more than one answer 15Polar form, De Moivres theorem and fraction in the power 16Complex Numbers 16 Proof of De Moivres Theorem by Induction 17Proof of Sin(3A) and Cos(3A)

Key ideas in this topic

The imaginary unit — The imaginary unitComplex Numbers

Modulus — ModulusComplex Numbers

The argument arg(z) — The argument arg(z)Complex Numbers

Polar form — Polar formComplex Numbers

De Moivre's theorem — De Moivre’s theoremin the log tables

Rules of polar form you must know

Multiplication — multiply the moduli, ADD the arguments — Multiplication — multiply the moduli, ADD the argumentsComplex Numbers 11

Division — divide the moduli, SUBTRACT the arguments — Division — divide the moduli, SUBTRACT the argumentsComplex Numbers 11

Reciprocal — the modulus inverts, the i-sign flips — Reciprocal — the modulus inverts, the i-sign flipsComplex Numbers 11

Transformations on the Argand plane

Scalar multiples — scaling along the line through O and z — Scalar multiples — scaling along the line through O and zk·z is collinear with z; |kz| = |k||z|

Rotations — Rotations×i = 90° anticlockwise, ×(−i) = 90° clockwise, ×(−1) = 180°

Addition — the parallelogram rule — Addition — the parallelogram ruleorigin, z₁, z₃, z₂ form a parallelogram

Conjugation — axial symmetry in the real axis — Conjugation — axial symmetry in the real axisz̄ is the mirror image of z across the real axis

Check it against the exam

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2023 Paper 1 Q3 →2023 Paper 1 Q4 →2022 Paper 1 Q1 →2022 Paper 1 Q3 →2021 Paper 1 Q1 →

Topic Content

0% Complete 0/17 Steps

Complex Numbers 1 – Introduction

Complex Numbers 2 – Addition, Subtraction, Multiplication

Complex Numbers 3 – Division and Conjugates

Complex Numbers 4 – Argand Plane and Modulus

Complex Numbers 5 – Modulus and conjugates

Complex Numbers 6 – Equating Co-efficients

Complex Numbers 7 – Rotations

Complex Numbers 8 – Quadratic equations

Complex Numbers 9 – Cubic equations

Complex Numbers 10: Introduction to Polar Form

Complex Numbers 11 – Rules for Polar Form

Complex Numbers 12 – Introduction to De Moivres theorem

Complex Numbers 13 – Converting to polar form and applying De Moivres theorem

Complex Numbers 14 – Using De Moivres theorem to find more than one answer

Complex Numbers 15: Polar form, De Moivres theorem and fraction in the power

Complex Numbers 16 Proof of De Moivres Theorem by Induction

Complex Numbers 17 – Proof of Sin(3A) and Cos(3A)