 Roadmap proposal for 3.10/4.0

Hans-Martin Mosner hmm at heeg.de
Tue Oct 17 19:31:39 UTC 2006

Damien Cassou schrieb:
> Ken Dickey a écrit :
>>   -4 sqrt. "2.0i"
>
> If I remember correctly what my math teacher taught me, this is
> incorrect.
>
>
> Rule of square roots:
> ---------------------
> a sqrt * b sqrt = (a*b) sqrt
>
> Applied to -4:
> --------------
> (-4) sqrt * (-4) sqrt = 16 sqrt = 4
>
> With your equality:
> -------------------
> (-4) sqrt * (-4) sqrt = 2i * 2i = -4
>
>
> We then have the same expression returning two different values. My
> teacher concluded saying "sqrt is a function only valid for positive
> numbers"
>
Your math teacher had a limited horizon (or you remember incorrectly).
I would rather conclude "the Rule of square roots is only valid for
positive numbers".
Additionally, remember that with only positive numbers, the square root
is defined as the positive solution to the equation x*x = a. There
always is a negative solution as well.

The equation x*x = 4 has two solutions, 2 and -2.
Similarly, x*x = -4 also has two solutions, 2i and -2i.
If you multiply these two, you get 4 (=16 sqrt).
Where's the problem? :-)

Cheers,
Hans-Martin