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Omni-MATH / Let a and b be complex numbers satisfying the two equations a³−3ab²=36 and b³−3ba²=28i. Let M be the maximum possible magnitude of a. Find all a such that |a|=M.

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problem

Let aa and bb be complex numbers satisfying the two equations a3−3ab2=36a^{3}-3ab^{2}=36 and b3−3ba2=28ib^{3}-3ba^{2}=28i. Let MM be the maximum possible magnitude of aa. Find all aa such that |a|=M|a|=M.
Plain-text mathematical notation (without MathML)
Let a and b be complex numbers satisfying the two equations a³−3ab²=36 and b³−3ba²=28i. Let M be the maximum possible magnitude of a. Find all a such that |a|=M.
Original LaTeX notation
Let $a$ and $b$ be complex numbers satisfying the two equations $a^{3}-3ab^{2}=36$ and $b^{3}-3ba^{2}=28i$. Let $M$ be the maximum possible magnitude of $a$. Find all $a$ such that $|a|=M$.

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Source and history

task_id
f9cbf9f9-c3f1-5611-9287-7dab5d88f4f5
task_key
test--f9cbf9f9-c3f1-5611-9287-7dab5d88f4f5
task_revision_id
1
config / split
/ test

Official source

initial import