Worksheets · Algebra 2

Multiplying complex numbers worksheet

Multiply two complex numbers exactly as you would two binomials, then use the one fact that makes them complex: i squared is -1. That turns the last term into an ordinary number, which then joins the real part.

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Pick more than one for a sheet that mixes them.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Multiplying Complex Numbers

Date Period

Simplify.

  1. (1+14i)(4+11i)
  2. (147i)(63i)
  3. (111i)(36i)
  4. (123i)(8+3i)
  5. (7+14i)(115i)
  6. (411i)(2i)
  7. (1314i)(610i)
  8. (13+13i)(14i)
  9. (5+8i)(1010i)
  10. (2+3i)(25i)
  11. (8+2i)(123i)
  12. (133i)(82i)
  13. (110i)(2+8i)
  14. (1214i)(133i)
  15. (1411i)(213i)
  16. (122i)(6+5i)
  17. (5+13i)(106i)
  18. (314i)(32i)
  19. (114i)(1213i)
  20. (6+5i)(8+12i)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Multiplying Complex NumbersAnswer keyVersion 1

Date Period

Simplify.

  1. (1+14i)(4+11i)150+67i
  2. (147i)(63i)63+84i
  3. (111i)(36i)63+39i
  4. (123i)(8+3i)105+12i
  5. (7+14i)(115i)7189i
  6. (411i)(2i)1918i
  7. (1314i)(610i)62214i
  8. (13+13i)(14i)195+169i
  9. (5+8i)(1010i)130+30i
  10. (2+3i)(25i)1116i
  11. (8+2i)(123i)102
  12. (133i)(82i)110+2i
  13. (110i)(2+8i)7828i
  14. (1214i)(133i)198146i
  15. (1411i)(213i)171+160i
  16. (122i)(6+5i)62+72i
  17. (5+13i)(106i)128+100i
  18. (314i)(32i)3736i
  19. (114i)(1213i)80+191i
  20. (6+5i)(8+12i)108+32i

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

(2+3i)(4i)

  1. Expand: 8 - 2i + 12i - 3i squared.
  2. i squared is -1, so -3i squared is +3.
  3. Collect: 8 + 3 and -2i + 12i.

The answer is 11+10i.

Where students go wrong

Leaving i squared in the answer, or treating it as +1. It is -1, and forgetting the minus flips the sign of the real part.

Also called multiplying imaginary numbers or product of complex numbers.

Questions about these worksheets

Yes. Every multiplying complex numbers sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the multiplying complex numbers questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Leaving i squared in the answer, or treating it as +1. It is -1, and forgetting the minus flips the sign of the real part.