Unit 1: Number and Algebra

Topic 1.12: Complex numbers: Cartesian (HL only) Questions

Practice 20 exam-style questions for IB Math AA SL Topic 1.12. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1Find2 marks
2026
Let z = 6 − 2i. Write down z* and find z × z*.
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2State2 marks
2026
Given (a + bi) = (2 + 3i) + (4 − i), state a and b.
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3Find3 marks
2026
Plot z₁ = 4 + 3i and z₂ = −1 − 2i on an Argand diagram and find |z₁|.
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41 mark
2026
(5 + 2i) − (3 − 4i) = ?
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51 mark
2026
Simplify i⁴.
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6Find2 marks
2026
Let z₁ = 4 − 3i and z₂ = −2 + 5i. Find z₁ + z₂ and z₁ − z₂.
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7Write down1 mark
2026
Write down .
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8Find2 marks
2026
Find the modulus of z = −6 − 8i.
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9Show that1 mark
2026
Show that .
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101 mark
2026
The point (0, −3) on an Argand diagram represents:
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111 mark
2026
The conjugate of −3 + 5i is:
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121 mark
2026
If |z| = 0, then z is:
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131 mark
2026
For which is z × z* NOT real?
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14Find2 marks
2026
Find |z| for z = 7 − 24i.
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15Find3 marks
2026
Find |z| for z = (1 + i)(2 − i).
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161 mark
2026
|−9 + 40i| = ?
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17Find3 marks
2026
A complex number z has |z| = 5 and its real part is 3 (with a positive imaginary part). Find z.
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181 mark
2026
Which complex number has the LARGEST modulus?
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191 mark
2026
The distance between the points 2 + 3i and 5 − i on an Argand diagram is:
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201 mark
2026
If z = a + bi and z = (1 − 2i)(2 + i), what is a?
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