MathGrit
ProblemsTechniquesPricing
Sign inGet started
Back to problems

Complex Function Integer Parts Counting

1675AdeptComplex NumbersCounting Principles

AMC 12A · 2013 · Problem 25

Let $f : \mathbb{C} \to \mathbb{C} $ be defined by $ f(z) = z^2 + iz + 1 $. How many complex numbers $z $ are there such that $ \text{Im}(z) > 0 $ and both the real and the imaginary parts of $f(z)$ are integers with absolute value at most $ 10 $?

Answer choices

A
399
B
401
C
413
D
431
E
441
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.AIME Practice StrategyHow to improve accuracy on high-difficulty problems.

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 Solutions1

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.