Ronan Downes, 14/03/2020

In addition, students working at HL should be able to – use the Conjugate Root Theorem to find the roots of polynomials – work with complex numbers in rectangular and polar form to solve quadratic and other equations including those in the form zn = a, where n ∈ Z and z = r (Cos θ + iSin θ ) – use De Moivre’s Theorem – prove De Moivre’s Theorem by induction for n ∈ N – use applications such as nth roots of unity, n ∈ N, and identities such as Cos 3θ = 4 Cos3 θ – 3 Cos θ

– appreciate that processes can generate sequences of numbers or objects – investigate patterns among these sequences – use patterns to continue the sequence – generalise and explain patterns and relationships in algebraic form – recognise whether a sequence is arithmetic, geometric or neither – find the sum to n terms of an arithmetic series

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In addition, students working at HL should be able to – use the Conjugate Root Theorem to find the roots of polynomials – work with complex numbers in rectangular and polar form to solve quadratic and other equations including those in the form zn = a, where n ∈ Z and z = r (Cos θ + iSin θ ) – use De Moivre’s Theorem – prove De Moivre’s Theorem by induction for n ∈ N – use applications such as nth roots of unity, n ∈ N, and identities such as Cos 3θ = 4 Cos3 θ – 3 Cos θ

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• 1. Roots of a complex number
• 2. Basic operations with complex numbers
• 3. Complex roots

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