EXN.1.AHL.TZ0.14

pestleMathematicsAIHLPaper 1EXN· ahl-1-12-complex-numbers-introductionsource ↗

Write down $2 + 5 i$ in exponential form.

[2]

An equilateral triangle is to be drawn on the Argand plane with one of the vertices at the point corresponding to $2 + 5 i$ and all the vertices equidistant from $0$ .

Find the points that correspond to the other two vertices. Give your answers in Cartesian form.

[3]

Markscheme / solution

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

$5.385 \dots e^{1.1902 \dots i} \approx 5.39 e^{1.19 i}$ A1A1

Note: Accept equivalent answers: $5.39 e^{- 5.09 i}$

[2 marks]

multiply by $e^{\frac{2 π}{3} i}$ (M1)

$- 5.33 - 0.77 i, 3.33 - 4.23 i$ A1A1

[3 marks]

Examiners’ report

[N/A]