Complex number — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses complex number — a algebra concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.

All of these problems are used with official legal permission of the Mathematical Association of America (MAA).

AMC 12

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

More algebra concepts

absolute valueagesalgebraic manipulationAM-GM Inequalityarithmetic sequencebinomial theoremcalculusCauchy-Schwarz Inequalitycompleting the squarecustom operationDe Moivre’s Theoremdeterminantdifference of squaresfactoringFibonaccifloor and ceiling functionsfunctionfunctional equationgeometric sequenceinequalitylinear equationlogarithmmatrixmixtureNewton’s Sumspartial fractionspolynomialquadraticradicalrational equationrationalizing denominatorrecursionroots of unitySimon’s Favorite Factoring Trickslopesubstitutionsum and difference of cubessum of first n cubessum of first n odd numberssum of first n squaressummationsymmetry (algebra)system of equationstelescopingVieta’s Formulas