2022TrialMultiple choice

Q10

1 mark

Question

In the diagram, the vectors $\overrightarrow{OP}$ and $\overrightarrow{OQ}$ represent the complex numbers $z_1$ and $z_2$ respectively. If
$\frac{z_2}{z_1}=\sqrt3\,i,$
what is the value of
$\left|\frac{z_1+z_2}{z_2-z_1}\right|?$

A. $1$
B. $\sqrt3$
C. $\frac1{\sqrt3}$
D. $\frac{\sqrt3+1}{\sqrt3-1}$

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Syllabus alignment

Complex Numbers

Geometrical implications of complex numbersInterpret complex-number operations geometrically and solve problems involving roots and loci in the complex plane.

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