GL Notes - Complex Numbers

https://glnotes.com/mathematics-extension-2/complex-numbers/

Explanation, Practise, Proof, Reference, Resources, Revision, Summary, Worksheet - Electronic

Complete online textbook, explanation and problems for Complex Numbers

10 May 2020 Edit: 10 May 2020

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Australian Curriculum / Specialist Mathematics:
Unit 2 Topic 3 Real and complex numbersComplex numbers:ACMSM067 define the imaginary number ii as a root of the equation x2=−1x2=-1ACMSM068 use complex numbers in the form a+bia+bi where aa and b b are the real and imaginary …ACMSM069 determine and use complex conjugatesACMSM070 perform complex-number arithmetic: addition, subtraction, multiplication and division…The complex plane:ACMSM071 consider complex numbers as points in a plane with real and imaginary parts as Cartes…ACMSM072 examine addition of complex numbers as vector addition in the complex planeACMSM073 understand and use location of complex conjugates in the complex plane.Roots of equations:ACMSM074 use the general solution of real quadratic equationsACMSM075 determine complex conjugate solutions of real quadratic equationsACMSM076 determine linear factors of real quadratic polynomials.Unit 3 Topic 1 Complex numbersCartesian forms:ACMSM077 review real and imaginary parts Re(z) Rez and Im(z)Im(z) of a complex number zzACMSM078 review Cartesian formACMSM079 review complex arithmetic using Cartesian forms.Complex arithmetic using polar form:ACMSM080 use the modulus ∣∣z∣∣zof a complex number z and the argument Arg (z)Arg (z) of a non-…ACMSM081 convert between Cartesian and polar formACMSM082 define and use multiplication, division, and powers of complex numbers in polar form …ACMSM083 prove and use De Moivre’s theorem for integral powers.The complex plane (the Argand plane):ACMSM084 examine and use addition of complex numbers as vector addition in the complex planeACMSM085 examine and use multiplication as a linear transformation in the complex planeidentify subsets of the complex plane determined by relations such as∣∣z−3i∣∣≤4z-3i≤4ACMSM086 π4≤Arg(z)≤3π4π4≤Arg(z)≤3π4, Re(z)>Im(z)Rez>Im(z) and ∣∣z−1∣∣=2∣∣z−i∣∣z-1=2Roots of complex numbers:ACMSM087 determine and examine the nthnth roots of unity and their location on the unit circleACMSM088 determine and examine the nthnthroots of complex numbers and their location in the co…Factorisation of polynomials:ACMSM089 prove and apply the factor theorem and the remainder theorem for polynomialsACMSM090 consider conjugate roots for polynomials with real coefficientsACMSM091 solve simple polynomial equations.
NSW Mathematics Extension 2 Stage 6 Syllabus:
Complex NumbersMEX-N1 Introduction to Complex NumbersMEX N1.1 Arithmetic of complex numbersMEX N1.2 Geometric representation of a complex numberMEX N1.3 Other representations of complex numbersMEX-N2 Using Complex NumbersMEX N2.1 Solving equations with complex numbers

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