IB Maths AI HL 1.12 Complex numbers Question Bank

Practise IB Mathematics HL 1.12 by applying complex numbers methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 4]

Nanthana is completing an exploration on multiplication using complex numbers. She considers a geometric sequence where $u_{1}=9$ and $r=\frac{2}{3}+\frac{2}{3} \mathrm{i}$ .

Show that Nanthana's claim is correct, stating the exact value of the common ratio for this sequence.

attempt to find |r|

\begin{aligned} & |r|=\sqrt{\left(\frac{2}{3}\right)^{2}+\left(\frac{2}{3}\right)^{2}} \\ & |r|=\frac{2 \sqrt{2}}{3} \end{aligned}

statement that multiplying a number by a complex number changes the modulus of the number by a factor of |r| (may be seen at any stage)

Note: Award at most (M1)A1A0R1 if common ratio is given as $0.942809 \ldots \ldots$ .
therefore it is a geometric sequence

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AHL 1.12 (HL)—Complex numbers question 1