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Complex numbers practice

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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Square each component, add the squares and take the nonnegative square root. Simplify the result exactly.

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A distance, not another complex number

For z = a + bi, the modulus is √(a² + b²). Its value is always real and nonnegative. A simplified radical preserves the exact answer when that distance is not an integer.

Each set contains ten questions. The key connects the squared components with the final simplified distance.

Learning objective

What this activity builds

Calculate the nonnegative distance of a complex number from the origin using its real and imaginary components.

Worked example

What is the absolute value of 6 − 8i?

10.

The distance is √(6² + (−8)²) = √100 = 10. The sign of the imaginary component changes direction, not distance.

Teaching notes

Make the practice count

  • Sketch the point and a right triangle before introducing the formula.
  • Square the signed component inside parentheses.
  • Keep a non-perfect root in exact form.
  • Compare a number with its conjugate: both have the same modulus.

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Math SheetNameScore/ 10TeacherDateAbsolute Values of Complex NumbersFind the absolute value of each complex number. Simplify each radical.1.|-9+3i|2.|6-9i|3.|6+4i|4.|-3+4i|5.|-4-2i|6.|-8-3i|7.|6-4i|8.|-5i|9.|-6+2i|10.|4-4i|math-sheet.comPage 1 / 1

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