A-Level Further Maths Edexcel (9FM0)

2: Complex numbers

#2.1

Solve quadratic, cubic and quartic equations

Find complex roots of quadratic equations

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Find complex roots of cubic equations

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Find complex roots of quartic equations

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#2.2

Complex numbers

Add and subtract complex numbers

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Multiply complex numbers

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#2.3

Complex conjugate

Divide complex numbers using the complex conjugate

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#2.4

Argand diagrams

Plot complex number on Argand diagram

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#2.5

Modulus-argument form of a complex number

Modulus-argument form of a complex number

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Convert modulus‑argument to Cartesian form

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Convert Cartesian to modulus‑argument form

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#2.6

Multiplication and division with modulus-argument form

Multiply and divide complex numbers in modulus-argument form

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#2.7

Loci in the Argand diagram

Equation of circle on Argand diagram

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Equation of perpendicular bisector on Argand diagram

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Equation of half-line on Argand diagram

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Represent regions on Argand diagrams using inequalities

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#2.8

De Moivre's theorem

Apply de Moivre's theorem for integer powers

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Use de Moivre's theorem to derive multiple‑angle trigonometric identities

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Use de Moivre's theorem for sums of geometric series

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#2.9

Exponential form of a complex number

Exponential form of a complex number and Euler's relation

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Multiply and divide complex numbers in exponential form

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#2.10

n distinct nth roots of a complex number

Find nth roots of a complex number

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Represent nth roots on Argand diagram

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#2.11

Complex roots of unity

Find nth roots of unity

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1

Proof

3

Matrices

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