Free Trial Session
Free Trial Session

Complex Numbers for Competitions: Geometry on the Argand Plane

The Master Guide to Rotations, Roots of Unity, and Euler’s Formula for AMC 12, AIME, and USAMO

Free

Stop Solving Geometry with Cartesian Coordinates. Start Using the Power of i.

In the world of high-level mathematics competitions—from the AMC 12 and AIME to the USAMO and JEE Advanced—Geometry problems are often designed to be a nightmare of messy calculations.

If you are still dropping perpendiculars and measuring angles the old-fashioned way, you are doing it the hard way. The top 1% of mathletes know a secret: Complex Numbers are not just Algebra. They are Geometry hacks.

Complex Numbers for Competitions is the tactical manual for the Argand Plane. Written by Rohan Kumar Singh (IIT Madras Alumnus & International Olympiad Gold Medalist), this book teaches you how to turn difficult geometry problems into elegant algebraic one-liners.

WHAT YOU WILL MASTER:

  • The Paradigm Shift: Stop seeing a + bi as numbers. Start seeing them as vectors, rotations, and dilations.

  • Rotational Geometry: Master the art of rotating points by multiplying by Euler's Form—the single most powerful tool in the Olympiad arsenal.

  • Roots of Unity: Visualize regular polygons on the unit circle and solve summation problems instantly.

  • The Heavy Hitters: Deep dive into Spiral Similarity, Ptolemy’s Inequality, and the Complex Shooter Theorem.

THE EDUGLOBAL METHOD

Based on the high-performance curriculum at EduGlobal Institute (home to 230+ Olympiad Rankers), this book respects your intelligence:

  1. Visual Diagnostics: Learn to identify when to use Complex Numbers vs. Synthetic Geometry.

  2. Concept Sprints: Rigorous theory on the Geometry of the Argand Plane.

  3. Speed Hacks: Specific shortcuts for calculating arguments and moduli.

  4. The Gauntlet: Real problems from AIME, USAMO, and RMO.

ABOUT THE AUTHOR

Rohan Kumar Singh is the Founder & Chief Mentor at EduGlobal Institute. An IIT Madras Alumnus and International Olympiad Gold Medalist, Rohan guides students to Ivy League admits and Gold Medals.

  • 1,200+ Students Mentored

  • 230+ Olympiad Rankers

  • 350+ AP 5/5 Scores

Geometry doesn't have to be messy. It can be beautiful.

Master Geometry on the Argand Plane today.