Level 3 Complex Numbers Walkthrough

2017 NCEA Level 3 Complex Numbers Question 1(a)

2017 Paper

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Question

If \(u=2+3i\) and \(v=1-4i\), find \(\overline{u}-3v\), giving your solution in the form \(a+bi\).

First walkthrough idea

Focus to try first

Conjugate \(u\), distribute the factor \(-3\), then collect the real and imaginary parts separately.

Step 1

Form the conjugate of u

Conjugation keeps the real part and reverses the sign of the imaginary part.

Show the first step’s working

For \(u=2+3i\), reflect the imaginary coordinate across the real axis:

\[ \overline{u}=2-3i. \]

Walkthrough overview

What this question practises

This 2017 walkthrough is part of AS91577 — Apply the algebra of complex numbers in solving problems.

Method: Conjugating a complex number, distributing a real factor, and collecting parts.

This is Question 1(a) from the 2017 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 conjugating a complex number, distributing a real factor, and collecting parts. 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(b) →