Senior 6 · UACE Mathematics

Complex numbers Past Questions & Worked Solutions

Q: Sample Question 2: Expressing complex numbers in modulus-argument polar form

The modulus is |z|=2. The point lies in quadrant II with reference angle \pi/3, so \arg z=2\pi/3. Hence z=2(\cos\tfrac{2\pi{3}+i\sin\tfrac{2\pi}{3})}.

Exam-style UACE Mathematics questions on Complex Numbers with step-by-step worked solutions for Senior 5–6 candidates preparing for UNEB examinations.

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Sample Questions

Worked Examples & Step-by-Step Solutions

Preview exam-style UACE Mathematics problems with full step-by-step solutions.

Sample Question 1: Multiplication and division of complex numbers in Cartesian form2 marks

Question

Express $(3+2i)(1-i)$ in the form $a+bi$ .

Step-by-Step Worked Solution

$(3+2i)(1-i)=3-3i+2i-2i^2=\boxed{5-i}.$

Sample Question 2: Expressing complex numbers in modulus-argument polar form4 marks

Question

Write $z=-1+\sqrt3i$ in polar form, using the principal argument.

Step-by-Step Worked Solution

The modulus is $|z|=2$ . The point lies in quadrant II with reference angle $\pi/3$ , so $\arg z=2\pi/3$ . Hence $\boxed{z=2(\cos\tfrac{2\pi}{3}+i\sin\tfrac{2\pi}{3})}.$

Complex numbers Past Questions & Worked Solutions

Worked Examples & Step-by-Step Solutions

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