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/sci/ - Science & Math

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4170921 No.4170921[DELETED]  [Reply] [Original]

Can anyone explain to me how we just extend the set of reals to include the complex numbers?

How does that even work?

>> No.4170941

http://en.wikipedia.org/wiki/Algebraic_closure

>> No.4170945
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4170945

What shitty quality op

>> No.4170952

You suppose that sqrt(-1) is a quantity called i, and you realise this is manipulatable and should be included for completeness.

Then, for example, sqrt(-4) = sqrt(4)*sqrt(-1) = 2i.

>> No.4170979
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4170979

>>4170921

Easy mode.

Take real number line. Put it on the x axis.

Take real number line times i. Put it on the y axis.

>> No.4170992

>>4170979

nah,
>>4170941

was more up my alley

>> No.4171060

C = {(a, b) € R^2}
*[C]: C x C -> C, (a,b) *[C] (c,d) |-> (a*c-b*d,a*d+b*c)
+[C]: C x C -> C, (a,b) +[C] (c,d) |-> (a+c,b+d)
Then (C, +[C], *[C]) is the field of the complex numbers.

>> No.4171077

>>4170921
to divide by zero. get roots of negative numbers and shit.