Complex numbers

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Understand and use the complex conjugate. Know that non-real roots of polynomial equations with real coefficients occur in conjugate pairs. Use and interpret Argand diagrams. Convert between the Cartesian form and the modulus-argument form of a complex number. Multiply and divide complex numbers in modulus argument form. Construct and interpret simple loci in the argand diagram such as |z − a| > r and arg (z – a) = θ. Understand de Moivre’s theorem and use it to find multiple angle formulae and sums of series. Know and use the definition eiθ = cos θ + i sin θ and the form z = reiθ Find the n distinct nth roots of reiθ for r ≠ 0 and know that they form the vertices of a regular n-gon in the Argand diagram. Use complex roots of unity to solve geometric problems.