Level 3 Complex Numbers Walkthrough

2025 NCEA Level 3 Complex Numbers Question 2(a)

2025 Paper

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Question

The complex numbers \(u\) and \(w\) are represented on the Argand diagram below.

Real Imaginary uw
\[ \text{If } z = 2u + 3w,\text{ find } z,\text{ and clearly show it on the Argand diagram above.} \]

First walkthrough idea

Focus to try first

reading complex numbers from an Argand diagram, scaling them, and adding them to find a new point.

Step 1

Read \(u\)

The point \(u\) is at \((4,2)\), so \(u=4+2i\).

Show the first step’s working

The point \(u\) is at \((4,2)\), so \(u=4+2i\).

Key result

\(\,u=4+2i\)

Walkthrough overview

What this question practises

This 2025 walkthrough is part of AS91577 — Apply the algebra of complex numbers in solving problems.

Method: Combining complex numbers from an Argand diagram.

This is Question 2(a) from the 2025 NCEA Level 3 Complex Numbers paper for AS91577 — Apply the algebra of complex numbers in solving problems. Use the guided hints to practise the method before revealing the full working.

Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91577.

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Learning summary

Review the method, not only the answer

This walkthrough helps you practise combining complex numbers from an Argand diagram. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Check each step against the original condition, preserve signs and restrictions, and confirm that the final result answers the question asked.

Continue practising

← Question 1(e) Question 2(b) →