Chapter 12: Further Pure 2: Complex Numbers

A-level Further MathsFurther Pure 1 & 23 topicsHigher

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Further Pure 2: Complex Numbers: Edexcel Further Maths Optional Long-Answer Questions

Examiner-style long-answer practice with automatic marking, improvement advice and ProofCoach tracking.

4 questions32 marks64 min

standard / hard / synoptic

8 marksfindstandardEdexcel

FP12-1 Find the required result for Further Pure 2: Complex Numbers. Given Find all fourth roots of 16(cos(2pi/3) + i sin(2pi/3)) and describe the locus |z - 2i| = |z - 4|. Use use De Moivre's theorem and geometric locus interpretation. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

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8 marksshow thathardEdexcel

FP12-2 Show that the roots have modulus 2 and arguments

\pi

/6, 2pi/3, 7pi/6, 5pi/3 for Further Pure 2: Complex Numbers. Start from Find all fourth roots of 16(cos(2pi/3) + i sin(2pi/3)) and describe the locus |z - 2i| = |z - 4|. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 marksdeterminehardEdexcel

FP12-3 Determine the requested value in this structured Further Pure 2: Complex Numbers problem: convert the locus to a Cartesian equation. Use the same data: Find all fourth roots of 16(cos(2pi/3) + i sin(2pi/3)) and describe the locus |z - 2i| = |z - 4|. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 markshencesynopticEdexcel

FP12-4 Hence use the result the roots have modulus 2 and arguments

\pi

/6, 2pi/3, 7pi/6, 5pi/3 to complete the extension for Further Pure 2: Complex Numbers: convert the locus to a Cartesian equation. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

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11. Further Pure 2: Groups

13. Further Pure 2: Recurrence Relations

Key learning objectives

Understand the key principles behind Further Pure 2: Complex Numbers.
Apply these ideas to exam-style questions.
Recall the essential definitions and key terms.