Unit 1: Number and Algebra
Topic 1.13: Complex numbers: continued (HL only) Questions
Practice 20 exam-style questions for IB Math AI SL Topic 1.13. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
To add two sinusoids of the SAME frequency, the quickest method is to:
Markscheme and model answer locked
Unlock Question6Find2 marks
2026
Find the modulus and argument of z = −4i.
Markscheme and model answer locked
Unlock Question71 mark
2026
In an AC circuit, the argument of the impedance Z = R + iX represents:
Markscheme and model answer locked
Unlock Question81 mark
2026
In which quadrant does z = −2 − 5i lie on the Argand diagram?
Markscheme and model answer locked
Unlock Question9Find3 marks
2026
z = √2 cis(135°). Use De Moivre's theorem to find z⁴, in the form a + bi.
Markscheme and model answer locked
Unlock Question10Find2 marks
2026
z₁ = 6 cis(35°) and z₂ = 4 cis(40°). Find z₁z₂, then state its modulus and argument.
Markscheme and model answer locked
Unlock Question11Express3 marks
2026
A current phasor is I = 2 + 2√3 i amps. Express it in the form r eiθ and interpret r and θ.
Markscheme and model answer locked
Unlock Question12Write2 marks
2026
Write z = 3 eiπ/3 in the form a + bi, giving exact values.
Markscheme and model answer locked
Unlock Question13Find2 marks
2026
Given z₁ = 5 cis(80°) and z₂ = 2 cis(20°), find z₁/z₂ in the form r cis θ.
Markscheme and model answer locked
Unlock Question141 mark
2026
To divide 10 cis(110°) by 5 cis(30°), you get:
Markscheme and model answer locked
Unlock Question16Interpret1 mark
2026
Interpret what raising a complex number to a power does geometrically.
Markscheme and model answer locked
Unlock Question17Write3 marks
2026
Write z = −1 + √3 i in the form r eiθ, where r > 0 and −π < θ ≤ π.
Markscheme and model answer locked
Unlock Question181 mark
2026
The resultant of phasors 9 + 0i and 0 + 12i has amplitude:
Markscheme and model answer locked
Unlock Question191 mark
2026
Multiplying a complex number by 2 eiπ/2 on the Argand diagram:
Markscheme and model answer locked
Unlock Question20Evaluate3 marks
2026
Use De Moivre's theorem to evaluate (√3 + i)⁶, giving your answer in the form a + bi.
Markscheme and model answer locked
Unlock QuestionReady to practice Topic 1.13?
Get instant AI feedback on your answers, view detailed markschemes, and track your progress across all IB Math AI SL topics.