CAIE A-Level Mathematics A2 3.9.2 Complex Numbers Questions

Practise arithmetic with complex numbers, including products, quotients and complex equations.

Exam points

perform arithmetic with complex numbers in Cartesian and polar forms
solve quadratic and algebraic equations over the complex numbers
simplify complex expressions and verify conjugate relationships

[Maximum number: 1]

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

Express $z \omega$ in the form a+b i, where a and b are real and in exact surd form.

State $z \omega=(-3+3 \sqrt{3})+(3+3 \sqrt{3}) \mathrm{i}$
Or exact equivalent with real and imaginary parts collected. Need brackets around the coefficient of i.

Marking guidance:

Allow for a=, b= stated correctly.

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CAIE A-Level Mathematics A2 3.9.2 Complex Numbers Questions question 1