Re: complex numbers

Dirk Van de moortel <dirkvandemoortel@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in
<VZfre.119624$ia5.6770755@xxxxxxxxxxxxxxxxxxxxx> on Monday 13 June 2005
08:36 posted to sci.physics.relativity:

>
> "N:dlzc D:aol T:com (dlzc)" <N: dlzc1 D:cox T:net@xxxxxxxxxx> wrote in
> message news:uLfre.7177$7s.91@xxxxxxxxxxxxx
>> Dear jem:
>>
>> "jem" <xxx@xxxxxxx> wrote in message
>> news:FVere.91014$sy6.84187@xxxxxxxxxxxxx
>> > The TimeLord wrote:
>> ...
>> >> You can see that unless you keep straight just what
>> >> the square root is defined to be,
>> >
>> > Sqrt() is defined to be a function so e.g. Sqrt(1) = 1,
>> > not +-1, and of course i^2 = -1, not +-1.
>>
>> sqrt() may be defined by programming languages to be "the
>> positive square root", allowing the programmer to assign whatever
>> sign(s) the programmer chooses. But the result of the square
>> root is bivalued
>
> Well, point me to *one* single technical or engineering
> publication or text in the world where they have an equation
> where they mean anything other than 3 when they write sqrt(9),
> and you are in business.
> sqrt is the positive root of a positive number.

The guy was asking about math, not engineering or tech stuff.

>
>> (except for sqrt(0) ). sqrt(-1) is the
>> conundrum, i^2 is the solution.
>
> There is no such thing as sqrt(-1).
> sqrt(-1) is for bad enceclopedias.

Definition:
Sqrt[-1] = i

>
>> And note that +/-i *is* a
>> solution, and valid result.
>
> Bot i and -i are things that give -1 when squared. You can
> safely forget everything else.

I don't know how safe it is to forget everything else. It's better to take
some care and get the correct answer than to rush to error like I did in my
first response (the conjugate issue), right?

--
// The TimeLord says:
// Pogo 2.0 = We have met the aliens and they are us!
.

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