Students will be able to
- understand that multiplication and division of complex numbers are often simpler in polar form than Cartesian (algebraic) form,
- understand the effect of multiplication and division on the argument and moduli of complex numbers,
- multiply and divide two (or more) complex numbers in polar form,
- multiply and divide two (or more) complex numbers in polar form and express the result in algebraic form,
- Extend the knowledge of multiplication and division of complex numbers in polar form to evaluate simple exponents, such as reciprocals, squares, and cubes.
Students should already be familiar with
- Cartesian and polar forms of a complex number,
- converting complex numbers between Cartesian and polar forms,
- Argand diagrams,
- complex conjugates and their properties.
Students will not cover
- questions only involving addition and subtraction of complex numbers,
- the exponential form of a complex number,
- de Moivre’s theorem.