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Convergent Complex Tetration Bases With the Most and Least Imaginary Parts - Printable Version

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Convergent Complex Tetration Bases With the Most and Least Imaginary Parts - Catullus - 07/10/2022

What number complex a has the largest imaginary part, such that a tetrated to the tower of x converges?
What number complex a has the most negative imaginary part, such that a tetrated to the tower of x converges?