Further Mathematics — Complex Numbers

Exam board: OCR  |  Back to subjects

Board-Specific Note

Frequently paired with the 'MEI' specification; strong applied component.

Learning Objectives

• Work with complex arithmetic
• Represent numbers on the Argand diagram
• Solve polynomial equations with complex roots

Key Points

• z = a + bi
• Conjugate z̄ = a − bi
• Argand diagram and modulus/argument
• Roots of quadratics come in conjugate pairs

Lesson Plan (50 minutes)

1. Starter (5 min): Recall prior knowledge of complex numbers with quick questions.
2. Teaching (15 min): Work through each of the learning objectives, explaining principles step by step.
3. Key points review (5 min): Revisit the key points together, confirming understanding.
4. Worked example (10 min): Model the example question: Solve z² + 4 = 0. Solution: z = ±2i
5. Practice (10 min): Students attempt the practice questions independently; circulate and support.
6. Plenary (5 min): Review answers and address misconceptions.

Homework

• Add 3+4i and 5−2i
• Multiply (2+i)(3−i)
• Solve z² + 2z + 5 = 0

Assessment

Check practice answers against the model answer; use the built-in practice questions as formative assessment.