- **Miscellaneous Math**
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- - **Pythagorean Theorem in Complex Numbers**
(*https://www.mersenneforum.org/showthread.php?t=26230*)

Pythagorean Theorem in Complex Numbers1 Attachment(s)
Hi All,
I am working through an unpublished number theory text book. Some university professors who are my friends wrote it. I want to share. I have found an example of complex numbers a, b and c such that a^2 + b^2 = c^2 But here the solution does not represent a length. Regards, Matt |

I have a set of complex a, b, c also:
3 + 0i, 4 + 0i, 5 + 0i. Edit: or 0 + 3i, 0 + 4i, 0 + 5i. |

There are algebraic formulas, e.g.
a = k*(p^2 - q^2), b = k*(2*p*q), c = k*(p^2 + q^2) for which a^2 + b^2 = c^2 is a polynomial identity. So k, p, and q can be rational integers, Gaussian integers, Eisenstein integers, arbitrary complex numbers, or just variables -- it's all good. There is a book entitled [u]Mathematics, Its Magic And Mastery[/u] by Aaron Bakst. One of its chapters is entitled [b]Algebra, Boss of Arithmetic[/b]. |

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