Chapter 1: Further Core Pure 1: Complex Numbers

A-level Further MathsFurther Core Pure5 topicsHigher

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Releases 1 August 2026

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Further Core Pure 1: Complex Numbers Long-Answer Questions

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4 questions24 marks36 min

standard / hard / synoptic

6 marksfindstandardEdexcel

FCP01-1: (3 + 2i)(1 - 4i). Find 11 - 10i for complex arithmetic and polynomial roots. Show the method clearly by using expand the brackets and use

i^{2}

= -1.

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6 marksshow thatstandardEdexcel

FCP01-2 verification: show that the printed answer is valid by applying expand the brackets and use

i^{2}

= -1. Include a check using (3 + 2i)(1 - 4i).

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6 marksprovehardEdexcel

FCP01-3 proof: starting with (3 + 2i)(1 - 4i), prove 11 - 10i for complex arithmetic and polynomial roots; give restrictions.

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6 markshencesynopticEdexcel

Using FCP01-4's earlier result 11 - 10i, hence solve the linked problem in complex arithmetic and polynomial roots and state whether the answer is exact or rounded.

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Start of Further Core Pure

2. Further Core Pure 1: Argand Diagrams

Key learning objectives

Understand the key principles behind Further Core Pure 1: Complex Numbers.
Apply these ideas to exam-style questions.
Recall the essential definitions and key terms.