Unit 3 Specialist Mathematics
Unit 3 of Specialist Mathematics contains three topics: ‘Vectors in three dimensions’, ‘Complex numbers’ and ‘Functions and sketching graphs’. The study of vectors was introduced in Unit 1 with a focus on vectors in two-dimensional space. In this unit, …
Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM080
use the modulus \(\left|z\right|\) of a complex number z and the argument \(Arg\;(z)\) of a non-zero complex number \(z\) and prove basic identities involving modulus and argument
ACMSM080 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM077
review real and imaginary parts \(Re\left(z\right)\;\) and \(Im(z)\) of a complex number \(z\)
ACMSM077 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM098
use and apply the notation \(\left|x\right|\) for the absolute value for the real number \(x\) and the graph of \(y=\left|x\right|\)
ACMSM098 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM086
identify subsets of the complex plane determined by relations such as \(\left|z-3i\right|\leq4\) \(\frac\pi4\leq Arg(z)\leq\frac{3\pi}4\), \(Re\left(z\right)>Im(z)\) and \(\left|z-1\right|=2\vert z-i\vert\)
ACMSM086 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum