Complex Numbers summary

Key learning points

• $z=x+iy$, $|z|=\sqrt{x^2+y^2}$, conjugate $x-iy$.
• Argand diagram: point $(x,y)$.
• Products/quotients are neat in polar form.
• Equate real and imaginary parts to solve equations.

Worked example 1 — Modulus

Find $|3-4i|$.

Working

3-4-5 triangle.

Worked example 2 — , , conjugate

Use this method from the Complex Numbers sheet: $z=x+iy$, $|z|=\sqrt{x^2+y^2}$, conjugate $x-iy$.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 3 — Argand diagram: point

Use this method from the Complex Numbers sheet: Argand diagram: point $(x,y)$.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 4 — Products/quotients are neat in polar form

Use this method from the Complex Numbers sheet: Products/quotients are neat in polar form.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 5 — Equate real and imaginary parts to solve equations

Use this method from the Complex Numbers sheet: Equate real and imaginary parts to solve equations.

Working

Each key learning point matches a question type on the printable worksheet.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.