MathGrit
ProblemsTechniquesPricing
Sign inGet started
Back to problems

Iterated Möbius transformation periodicity

1925SpecialistComplex NumbersFunctions

AIME I · 2002 · Problem 12

Let $F(z)=\frac{z+i}{z-i}$ for all complex numbers $z\not= i$, and let $z_n=F(z_{n-1})$ for all positive integers $n$. Given that $z_0=\frac 1{137}+i$ and $z_{2002}=a+bi$, where $a$ and $b$ are real numbers, find $a+b$.
0 students attempted0% solvedRating 1925

Related practice paths

AIME PracticeInteger-answer practice for deeper multi-step problems.How to Qualify for AIMEScore goals, contest choice, and prep habits for AIME hopefuls.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 Solutions10

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.