CAIE A-Level Mathematics A2 3.9.5 Complex Numbers Questions

Practise using modulus–argument and exponential forms to multiply, divide and raise complex numbers to powers.

Exam points

convert complex numbers between Cartesian, modulus–argument and exponential forms
use arguments and moduli in products, quotients and powers
solve trigonometric and algebraic results from exponential complex forms

[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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CAIE A-Level Mathematics A2 3.9.5 Complex Numbers Questions question 1