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AIME 2024 / AIME 2024 train 2f1a86c8-ce3e-5f8d-90e1-774ad3aa4a3f

Problem

Answer published by the source. Consult the official source to check your work against its answer.

Problem

Find the largest possible real part of

(75+117i)z + \frac{96+144i}{z}

where

z

is a complex number with

|z|=4

Plain-text mathematical notation (without MathML)

Find the largest possible real part of (75+117i)z+(96+144i)/(z) where z is a complex number with |z|=4.

Original LaTeX notation

Find the largest possible real part of \[(75+117i)z + \frac{96+144i}{z}\] where $z$ is a complex number with $|z|=4$.

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Source and history

task_id: 2f1a86c8-ce3e-5f8d-90e1-774ad3aa4a3f
task_key: default--train--2f1a86c8-ce3e-5f8d-90e1-774ad3aa4a3f
task_revision_id: 2
config / split: default / train

Official source

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