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NSW Syllabus Reference: MEX-N1.3: Other Representations of Complex Numbers
In this section of the syllabus, you will need to
1. Understand Euler’s formula, \(e^{ix}=\cos x+i\sin x\) for real \(x\)
2. Represent and use complex numbers in exponential form, \(z=re^{i\theta\), where \(r\) is the modulus of \(z\) and \(\theta\) is the argument of \(z\)
3. Use Euler’s formula to link polar form and exponential form
4. Convert between Cartesian, polar and exponential forms of complex numbers
5. Find powers of complex numbers using exponential form
6. Use multiplication, division and powers of complex numbers in polar form and interpret these geometrically
7. Solve problems involving complex numbers in a variety of forms