I should be able to:
Ordinary Level
– * investigate the operations of addition, multiplication, subtraction and division with complex numbers C in the form a+ib ka.4.4.1
– * illustrate complex numbers on an Argand diagram ka.4.4.1
– * interpret the modulus as distance from the origin on an Argand diagram and calculate the complex conjugate ka.4.4.1
Higher Level
– * calculate conjugates of sums and products of complex numbers
– use the Conjugate Root Theorem to find the roots of polynomials ka.4.4.1
– work with complex numbers in rectangular and polar form to solve quadratic and other equations including those in the form zn= a, where n ∈ Z and z = r Cos θ + iSin θ
– use De Moivre’s Theorem
– prove De Moivre’s Theorem by induction for n ∈ N
– use applications such as nth roots of unity, n ∈ N and identities such as Cos 3θ = 4 Cos3θ – 3 Cos θ
* Note these outcomes have already been listed in the section 3.1 Number Systems
Presentation from Project Maths
Geogebra Adding & Subtracting on an Argand Diagram
Geogebra Multiplication on an Argand Diagram
Geogebra Multiplication on an Argand Diagram with Focus on Modulus