Complex numbers
Absolute value of complex numbers worksheets
Find the modulus of ten complex numbers. Connect real and imaginary components with distance from the origin, then check exact, simplified radical answers.
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Complex numbers review worksheets
Combine four modulus questions with four complex-plane questions. Choose plotting, identifying points or both, with a separate key for the same generated set.
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Find the four absolute values first. Then complete the graph questions using the real and imaginary axes.
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Check two skills in one set
The first four questions ask for a modulus. The next four ask learners to plot or identify complex numbers, so you can see whether they connect the algebraic notation with the plane.
Mixed mode supplies two plot and two identify questions after the four modulus questions. Use a focused sheet again if one section reveals a gap.
Learning objective
What this activity builds
Move between the algebraic form, position and distance of a complex number.
Worked example
Describe −4 + 3i by its position and modulus.
Its point is (−4, 3) and its modulus is 5.
The components locate the point. The distance from the origin is √(16 + 9) = 5; this is a different question from identifying either coordinate.
Teaching notes
Make the practice count
- Use the two sections to distinguish a coordinate error from a distance error.
- Ask for an explanation of one modulus calculation.
- Alternate plot-only and identify-only sets before using a mixture.
- Compare an answer with a sketch before moving to a new set.
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Customize the practice
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Add, subtract and multiply complex numbers in ten-question sets. Select sums and differences, imaginary monomial products or binomial products and squares.
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