Re: complex numbers
- From: jem <xxx@xxxxxxx>
- Date: Tue, 14 Jun 2005 08:28:14 -0400
N:dlzc D:aol T:com (dlzc) wrote:
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 (except for sqrt(0) ). sqrt(-1) is the conundrum, i^2 is the solution. And note that +/-i *is* a solution, and valid result.
Dear Mr. Smith,
The equation x^2 = a does indeed have 2 roots (even for a=0 according to the Fundamental Theorem of Arithmetic), but the *functional* relationship x = sqrt(a) has only 1 root.
.
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