Triangle area in complex plane

1675AdeptComplex NumbersGeometry

AMC 12B · 2025 · Problem 22

What is the greatest possible area of the triangle in the complex plane with vertices $2z$, $(1+i)z$, and $(1-i)z$, where $z$ is a complex number satisfying $|4z - 2| = 1$?

Answer choices

~\frac 14

~\frac 12

~\frac{9}{16}

~\frac 34

0 students attempted0% solvedRating 1675

Related practice paths

AMC 12 PracticeAdvanced high school contest practice and review.AMC 10 vs AMC 12Choose the right practice path and difficulty level.How to Review Missed AMC ProblemsTurn missed problems into a repeatable improvement loop.

Ready to check your answer?

Create an account to submit answers, save history, and track your rating.

Progressive Hints5

Unlock hints one at a time — each reveals a little more without spoiling the solution.

Step-by-Step Solutions12

Multiple solution approaches with detailed walkthroughs, unlocked after you solve the problem.

AI-Powered Grading

Instant feedback on your answer — handles fractions, decimals, and equivalent forms.

Curated problem bank

Supported tracks for AMC, AIME, MATHCOUNTS, and olympiad-style training, plus global problem sources like UKMT, Euclid, and Kangaroo.