Unit 1: Number and Algebra

Topic 1.13: Complex numbers: polar (HL only) Questions

Practice 20 exam-style questions for IB Math AA 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
(4 cis(π/3))(2 cis(π/6)) = ?
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21 mark
2026
The argument of −4 (as a complex number) is:
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31 mark
2026
Write 5 cis(π) in Cartesian form.
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41 mark
2026
Which is in quadrant 2 of the Argand diagram?
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5Find3 marks
2026
Find (3 cis(π/5))(4 cis(2π/5)) in polar form.
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6Express3 marks
2026
Write z = 1 + i in exponential form.
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7Find1 mark
2026
Find .
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8Write down1 mark
2026
Write down and .
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91 mark
2026
Write 7 cis(2π/3) in exponential form.
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10Express2 marks
2026
Write z = −7 in polar form (−π < θ ≤ π).
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11Express2 marks
2026
Write z = 3 cis(π/2) in Cartesian form.
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121 mark
2026
Multiplying by 2 cis(π) does what to a point?
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131 mark
2026
If z = 3 cis(π/4), then z × z* (using polar) is:
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141 mark
2026
To rotate a point 60° clockwise about the origin, multiply by:
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15Express3 marks
2026
Write z = 6 eiπ/3 in Cartesian form.
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16Find3 marks
2026
Find (5 eiπ/6)(2 eiπ/3) in exponential form.
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171 mark
2026
(3 eiπ/5) × (3 ei4π/5) = ?
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18Find3 marks
2026
Find (12 ei2π/3)/(3 eiπ/6) in exponential form.
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19Show2 marks
2026
Show that eiπ/2 = i.
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20Find2 marks
2026
Find in modulus-argument form.
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