McIntyre MathsMathematics Extension 2
Extension 2 › Complex Numbers I

Complex Numbers I Term 4 Week 6 to Term 1 Week 2 · 10 lessons

Introduction to complex numbers

Outcomes MAO-WM-01, ME2-12-03

Lessons

Lesson 1The arithmetic of complex numbersThe number i, the number sets, and adding, subtracting and multiplying complex numbersReadyLesson 2Conjugates, division and equalityThe conjugate and modulus, dividing complex numbers, and equating real and imaginary partsReadyLesson 3Quadratic equations and square rootsSolving quadratics with complex roots and finding the square roots of a complex numberReadyLesson 4The Argand diagramPlotting complex numbers, multiplication by i as a rotation, and simple lociReadyLesson 5Modulus–argument formModulus, argument and principal argument, and converting between Cartesian and polar formReadyLesson 6Multiplying and dividing in polar formMultiply, divide and take powers in polar form, and prove the modulus and argument rulesReadyLesson 7Complex numbers as vectorsRepresent complex numbers as vectors, add and subtract them geometrically, and prove the triangle inequalityReadyLesson 8Rotation, dilation and geometryUse multiplication as rotation and dilation to find vertices and prove geometric resultsReadyLesson 9Lines and circles in the Argand diagramSketch circles, discs and perpendicular bisectors defined by modulus conditionsReadyLesson 10Rays and regionsSketch rays and regions defined by argument and modulus conditions, and find greatest and least valuesReady