Kenneth ChengMathematical modeling
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Find the real part using de Moivre’s formula.

Read the idea, work independently, then explain what changed.

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TOPIC 01

Complex numbers: mixed assessment

A mixed assessment: identify the method, justify it and revise your reasoning.

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

Find the real part using de Moivre’s formula.

[7(cos⁡(π/3)+isin⁡(π/3))]3[7(\cos(\pi/3)+i\sin(\pi/3))]^3
  • Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Use modulus and argument, remembering that arguments differ by full turns.
Hint 2
Cube the modulus and triple the angle.
Worked solution

  1. Use modulus and argument, remembering that arguments differ by full turns.

  2. Calculate or simplify this relation.

    343(cos⁡π+isin⁡π)=−343343(\cos\pi+i\sin\pi)=-343

  3. The angle multiplication must accompany the modulus power.

The requested value is -343.

Checks and common pitfalls: The angle multiplication must accompany the modulus power.

Think first. Reveal a hint when the class is ready.

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗