AMC complex numbers problems

Complex arithmetic, roots of unity and De Moivre's theorem.

59 problems in the archive use these ideas — 1 from the AMC 10 and 58 from the AMC 12.

Picks a problem you have not seen, at about the difficulty you are handling.

Problems

Newest contests first. Every problem opens with its answer choices, hints and a worked solution.

2025 AMC 12A · Problem 9
2025 AMC 12A · Problem 17
2025 AMC 12B · Problem 3
2025 AMC 12B · Problem 22
2024 AMC 12A · Problem 15
2024 AMC 12B · Problem 12
2023 AMC 10B · Problem 21
2023 AMC 12A · Problem 14
2023 AMC 12A · Problem 16
2023 AMC 12A · Problem 25
2023 AMC 12B · Problem 12
2023 AMC 12B · Problem 19
2022 AMC 12A · Problem 21
2022 AMC 12A · Problem 22
2022 AMC 12B · Problem 11
2022 AMC 12B · Problem 24
2021 AMC 12A · Problem 13
2021 AMC 12A · Problem 15
2021 AMC 12A · Problem 21
2021 AMC 12A · Problem 22
2021 AMC 12B · Problem 18
2021 AMC 12B · Problem 20
2021 Fall AMC 12A · Problem 15
2021 Fall AMC 12A · Problem 25
2021 Fall AMC 12B · Problem 21
2020 AMC 12A · Problem 15
2020 AMC 12A · Problem 22
2020 AMC 12B · Problem 17
2020 AMC 12B · Problem 23
2019 AMC 12A · Problem 14
2019 AMC 12A · Problem 21
2019 AMC 12B · Problem 17
2019 AMC 12B · Problem 24
2018 AMC 12A · Problem 22
2018 AMC 12B · Problem 16
2017 AMC 12A · Problem 17
2017 AMC 12A · Problem 25
2017 AMC 12B · Problem 12
2015 AMC 12A · Problem 24
2015 AMC 12B · Problem 25
2013 AMC 12A · Problem 25
2013 AMC 12B · Problem 25
2012 AMC 12B · Problem 23
2011 AMC 12A · Problem 23
2011 AMC 12B · Problem 24
2010 AMC 12B · Problem 15
2009 AMC 12A · Problem 15
2009 AMC 12A · Problem 21
2009 AMC 12B · Problem 23
2008 AMC 12A · Problem 23
2008 AMC 12A · Problem 25
2008 AMC 12B · Problem 19
2007 AMC 12A · Problem 18
2005 AMC 12B · Problem 22
2004 AMC 12A · Problem 23
2004 AMC 12B · Problem 16
2002 AMC 12A · Problem 24
2001 AMC 12 · Problem 23
2000 AMC 12 · Problem 22

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