Applications & Interpretation HL · Topic 1 · Number & Algebra

IB Math AI HL Further Complex Numbers Worksheet (questions only)

HL complex numbers: de Moivre's theorem, roots of unity, nth roots and proving trigonometric identities.

24 pages · 120 marks · questions only · free PDF for IB Mathematics: Applications and Interpretation HL students.

24pages
120marks
3difficulty levels
Nosolutions included
T1Number & Algebra

Download the AI HL Further Complex Numbers worksheet (PDF) ↓   All AI HL worksheets →

What this AI HL further complex numbers worksheet covers

HL complex numbers: de Moivre's theorem, roots of unity, nth roots and proving trigonometric identities. The questions follow the order of the AI HL syllabus for Topic 1 (Number & Algebra) and are graded in three bands — routine practice, exam-standard, and the harder multi-step questions that separate a 6 from a 7.

De Moivre's theorem for powers and roots
nth roots of a complex number on the Argand diagram
Roots of unity and their sum
Using complex numbers to prove trigonometric identities
Exam tip for this topic. Find all n roots by adding 2πk/n to the argument — a diagram with the roots equally spaced is worth drawing.

Preview

How to use it

  1. Do the first band without the AI HL formula booklet, then check which formulas you had to look up — those are the ones to memorise.
  2. Time the second band at roughly 1.2 minutes per mark, the pace of Paper 1 and Paper 2.
  3. For the third band, compare your method with the matching questions in the AI HL question bank; if you want this set marked, send it to Mr Ahmad.

More AI HL worksheets on Number & Algebra

✓ = solutions included

The same topic for other courses

Questions

Is this AI HL further complex numbers worksheet free?

Yes — download the PDF with no sign-up. It is one of over 130 free IB Math worksheets on this site, written to match the current syllabus.

Does it come with answers?

This set is questions only. If you would like it marked, or want the matching solutions, contact Mr Ahmad.

Which IB course is it for?

IB Mathematics: Applications and Interpretation HL. The same topic is also available for the other courses where it is on the syllabus — see the links above.

Stuck on a question from this sheet?

Mr Ahmad tutors IB Mathematics: Applications and Interpretation HL students in Dubai and online — topic drills like this one, past-paper technique and IA support.

Book a 50% Off Trial Lesson →
Mr. Ahmad · IB Maths TutorAsk me anything about lessons