A-Level Further Maths Edexcel 9FM0

Solve any quadratic equation with real coefficients.

Solve cubic or quartic equations with real coefficients.

Add, subtract, multiply and divide complex numbers in the form $x + \text{i}y$ with $x$ and $y$ real.

Understand and use the terms "real part" and "imaginary part".

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 $\text{arg} (z - a) = θ$.

Understand de Moivre's theorem and use it to find multiple angle formulae and sums of series.

Know and use the definition $e^{\text{i}θ} = \cos{θ} + \text{i} \sin{θ}$ and the form $z = re^{\text{i}θ}$

Find the n distinct $n$th roots of $re^{\text{i}θ}$ 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.