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NSW Syllabus Reference: MEX-N2.2: Geometrical Implications of Complex Numbers
This NSW syllabus reference for Vector Problems focuses on point 1
1. examine and use addition and subtraction of complex numbers as vectors in the complex plane (ACMSM084)
2. examine and use the geometric interpretation of multiplying complex numbers, including rotation and dilation in the complex plane
3. recognise and use the geometrical relationship between the point representing a complex number \(z=a+ib\), and the points representing \(\overline z \), \(cz\) (where is real) and \(iz\).
4. determine and examine the \(n^{th}\) roots of unity and their location on the unit circle (ACMSM087)
5. determine and examine the \(n^{th}\) roots of complex numbers and their location in the complex plane (ACMSM088)
6. solve problems using \(n^{th}\) roots of complex numbers
7. identify subsets of the complex plane determined by relations, for example \(|z-3i|\le4,\, \dfrac{\pi}{4}\le Arg(z)\le\dfrac{3\pi}{4},\, Re(z)>Im(z)\) and \(|z-1|=2|z-i|\) (ACMSM086)