Multiply moduli, add arguments: To multiply two complex numbers in polar form: multiply the moduli and add the arguments.
Geometrically, multiplying by r cisθ scales by r and rotates by θ.
Multiplying by i (= cis 90°) rotates the point 90° anticlockwise — angles add.
Interactive diagram
Explore the labelled diagram, charts and maps for this topic in full study mode.
IB-style question — multiply in polar form
Find (2 cis(π/6))(3 cis(π/4)), giving your answer in polar form.
Step by step
- Multiply the moduli.
- Add the arguments.
- Combine.
Final answer
6 cis(5π/12).
Free preview
This is the free notes preview
You're reading the free notes. Aimnova Pro unlocks the full study experience — and you can try it free for 7 days:
- FlashcardsLock in vocabulary and key terms with spaced repetition.
- Practice questionsAnswer exam-style questions and get instant AI marking.
- Mock exams & past-paper vaultSit full mocks and see exactly how examiners award marks.
- Personalised study planA daily plan built around your exam date and weak areas.
Start your 7-day free trial Full access to Aimnova Pro · cancel anytime
Divide moduli, subtract arguments: To divide, divide the moduli and subtract the arguments (top minus bottom). Much easier than the conjugate method when you're already in polar form.
IB-style question — divide in polar form
Find (12 cis(2π/3))/(4 cis(π/4)), giving your answer in polar form.
Step by step
- Divide the moduli.
- Subtract the arguments (top − bottom).
- Combine.
Final answer
3 cis(5π/12).