Complex Numbers
1. Irrational numbers
Irrational numbers  surds 

Construct root 2Using a compass and straight edge


Construct root 3Using a compass and straight edge


2. Complex numbers introduction
Equation with imaginary roots 

Quadratic equation with imaginary rootsUsing the quadratic formula


Addition and multiplication of complex numbers 

3. Division and equity of complex numbers
Dividing by a complex number  conjugateExpressing a fraction with a real denominator


Complex number equations"Real = real, imaginary = imaginary"


4. Argand diagram  modulus
Plot on an Argand diagram


5. Transformations of complex numbers
Understanding multiplication 

Multiplication involves scaling and rotating


Transformations involving multiplication 

6. Conjugate roots theorem
Quadratic equation  conjugate roots 

Showing that a conjugate is a root 

Solving a cubic equation with two imaginary roots 

7. Polar form of a complex number
Converting from polar to rectangular form 

Express in polar formFinding the modulus and argument


8. Products and quotients in polar form
Multiplying and dividing in polar formMultiplication: Multiply the module and add the arguments
Division: Divide the module and subtract the arguments


9. De Moivre's Theorem
Raising a number to a power  expanding 

Express in polar form and expand 

10. Applications of de Moivre's Theorem
Raising a number to a power 

Proving trigonometric identities using de Moivre's Theorem 

Finding roots 

12 Revision Questions 
Complex Number Video
Powers of i


Introduction to Complex Numbers: Addition, subtraction, multiplication, powers of i.


Complex division in rectangular form


Solving Complex Equations:
Real parts = Real parts Imaginary parts = Imaginary parts 

Graphing complex numbers on an Argand diagram and finding the modulus of a complex number.


Transformations in the Complex Plane


Complex conjugate roots
Solving quadratic and cubic equations with imaginary roots. 

Writing a complex number in Polar Form


Multiplying and dividing in Polar Form and using deMoivre's Theorem to expand a complex number to a power.


Using deMoivre's Theorem to find roots of a Complex Equation.


Using deMoivre's Theorem to prove Trigonometric identities. This question also requires use of the Binomial Theorem.

