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November 14th, 2010, 05:42 AM   #1
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the history behind complex numbers

So I read the first chapter of Complex Analysis by Matthews and Howell. There were two questions that got me speechless in the Exercises for Section 1.1. Those questions were...

Explain why cubic equations, rather than quadratic equations, played a pivotal role in helping to obtain the acceptance of complex numbers.

and

Explain why Wallis's view of complex results in being represented by the same point as is .

I don't think the book explained the reason why. Can someone explain this to me?
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November 15th, 2010, 03:51 PM   #2
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Re: the history behind complex numbers

I don't actually know who Wallis is, but I can talk on the first one a little bit. It turns out that the general solution for the cubic can, upon occasion, involve square roots of negative numbers. But the solution works, and in some such occasions the square roots of negative numbers might cancel, mathematically. So why not allow them to exist if they work in a formula, rather than making it explode (like dividing by zero, for example, which ruins everything)?
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November 23rd, 2010, 07:25 PM   #3
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Re: the history behind complex numbers

To add to jason.spade's reply, look up Casus irreducibilis on Wikipedia or elsewhere.
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