Analysis & Approaches HL · Topic 1 · Number & Algebra

IB Math AA HL Complex Numbers Worksheet (with full solutions)

Cartesian, polar and Euler forms, the Argand diagram and operations with complex numbers.

22 pages · 120 marks · with full solutions · free PDF for IB Mathematics: Analysis and Approaches HL students.

22pages
120marks
3difficulty levels
Yessolutions included
T1Number & Algebra

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What this AA HL complex numbers worksheet covers

Cartesian, polar and Euler forms, the Argand diagram and operations with complex numbers. The questions follow the order of the AA 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.

Addition, multiplication and division in Cartesian form
Modulus and argument; converting between forms
Multiplying and dividing in polar form
Solving quadratics with complex roots
Exam tip for this topic. Check the quadrant of the argument from a sketch — the calculator's tan⁻¹ only covers two quadrants.

Preview

How to use it

  1. Do the first band without the AA 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. Mark the third band against the solutions and rewrite every question you lost marks on from a blank page.

More AA HL worksheets on Number & Algebra

✓ = solutions included

The same topic for other courses

Questions

Is this AA HL 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?

Yes, full worked solutions are included at the end of the PDF.

Which IB course is it for?

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

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