CAIE A-Level Mathematics A2 3.9.1 Complex Numbers Questions

Practise modulus, argument and polar forms for complex numbers in the AS mathematics syllabus.

Exam points

express complex numbers in Cartesian and polar forms
calculate modulus and argument with correct ranges
convert between complex-number representations

[Maximum number: 4]

The complex numbers z and $\omega$ are defined by z=1-i and $\omega=-3+3 \sqrt{3} \mathrm{i}$ .

Express z and $\omega$ in the form $r \mathrm{e}^{\mathrm{i} \theta}$ , where r>0 and $-\pi<\theta \leqslant \pi$ . Give the exact values of r and $\theta$ in each case.

Obtain $|z|=\sqrt{2}$
Obtain $\arg z=-\frac{\pi}{4}$ final answer
Obtain $|\omega|=6$
Obtain $\arg \omega=\frac{2 \pi}{3}$ final answer

All question bank results loaded

CAIE A-Level Mathematics A2 3.9.1 Complex Numbers Questions question 1