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Complex Conjugate Root Theorem (Formal Proof)

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However, Diophantus gave indications that he had no conception of the abstract notion of negative number [S, ] [C, 61]. Seventh Century C. He gave rules for operations with negative numbers.

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Ninth Century C. E, Middle East.

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Thus his discussion of quadratic equations dealt with six different types of equations, rather than the one general form we use. Twelfth Century, India : Bhaskara gives negative roots for quadratic equations, but says the negative value "is in this case not to be taken, for it is inadequate; people do not approve of negative roots.

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Thirteenth Century, China : Negative numbers were indicated by drawing a diagonal stroke through the right-most nonzero digit of a negative number. However, Mark Dominus private communication has pointed out that in Sigler's English translation of Liber Abaci there are some problems that do involve negative solutions, which are interpreted as debits.

Fifteenth Century, Europe : Chuquet was the first to use negative numbers in a European work.

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However, he referred to them as "absurd numbers.