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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_13 / Let R be the region in the complex plane consisting of all complex numbers z that can be written as the sum of complex numbers z₁ and z₂, where z₁ lies on the segment with endpoint…

Problem

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problem

Let

\mathcal{R}

be the region in the complex plane consisting of all complex numbers

z

that can be written as the sum of complex numbers

z_1

and

z_2

, where

z_1

lies on the segment with endpoints

3

and

4i

, and

z_2

has magnitude at most

1

. What integer is closest to the area of

\mathcal{R}

Plain-text mathematical notation (without MathML)

Let R be the region in the complex plane consisting of all complex numbers z that can be written as the sum of complex numbers z₁ and z₂, where z₁ lies on the segment with endpoints 3 and 4i, and z₂ has magnitude at most 1. What integer is closest to the area of R?

Original LaTeX notation

Let $\mathcal{R}$ be the region in the complex plane consisting of all complex numbers $z$ that can be written as the sum of complex numbers $z_1$ and $z_2$, where $z_1$ lies on the segment with endpoints $3$ and $4i$, and $z_2$ has magnitude at most $1$. What integer is closest to the area of $\mathcal{R}$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_13
task_id: dbdcc017-c92b-51dc-bc7c-6e25bfbc9913
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f13
task_revision_id: 2
config / split: default / train

Official source

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