CAIE A-Level Mathematics 3.9.5 Complex numbers

Practise multiplying, dividing and powering complex numbers in polar or exponential form, tracking exact moduli and arguments.

Exam points

combine moduli and arguments to express products or quotients as re^{iθ}

[Maximum number: 2]

The complex number u is given by $u=-1-\mathrm{i} \sqrt{3}$ .

Express the complex number $\frac{v}{u}$ in the form $r \mathrm{e}^{\mathrm{i} \theta}$ where r>0 and $-\pi<\theta \leqslant \pi$ .

State or imply $r=\frac{5}{2}$

B1FT

FT $\frac{5}{\text { their } 2}$ .

State or imply $\theta=\frac{5}{6} \pi$

B1FT

FT $\frac{1}{6} \pi-$ their $-\frac{2}{3} \pi$ .

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3.9.5—Complex numbers question 1