Level 3 Complex Numbers Walkthrough

2025 NCEA Level 3 Complex Numbers Question 1(b)

2025 Paper

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Question

\[ x^2 - 6kx = k^2 \]

Solve the equation for \(x\).

Simplify your answer as far as possible, giving your answer in terms of \(k\).

First walkthrough idea

Focus to try first

rearranging a quadratic in \(x\), completing the square, and solving in terms of \(k\).

Step 1

Identify the equation type

The highest power of \(x\) is \(2\), so we are solving a quadratic.

Show the first step’s working

The highest power of \(x\) is \(2\), so we are solving a quadratic.

Key result

A quadratic equation.

Walkthrough overview

What this question practises

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

Method: Completing the square and solving in terms of \(k\).

This is Question 1(b) 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 completing the square and solving in terms of \(k\). 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(a) Question 1(c) →