Re: how can I return nothing?

Richard Heathfield wrote:
Michal Nazarewicz said:

richard@xxxxxxxxxxxxxxx (Richard Tobin) writes:

In article <1xgzve9ftnef0.qkfno80gbnsf.dlg@xxxxxxxxxx>,
Coos Haak <chforth@xxxxxxxxx> wrote:

i nor -i is the square root of -1.
What makes you think that?
The same thing I've pointed. In real number domain a square root of
x is defined to be _nonnegative_ number which squared gives x. You
cannot apply analogical definitions to complex numbers since there is no
such think as nonnegative complex number (or nonpositive for that
matter).

Sorry, but I must disagree. I can accept that there is no such thing as a positive imaginary number, and no such thing as a negative imaginary number,

Im(z) has a sign, just like Re(z) do.

but I cannot accept that there is no such thing as a non-negative *complex* number.


Just view a complex number as a vector, the useful properties of a vector is the direction and magnitude. Those properties fully describe it in a N-dimensional case too, no matter what coordinate system you use.


A complex number has a (possibly zero but usually not) real number element which is sufficient to displace it off the zero line in the complex plane. Most numbers in the complex plane are either to the right of the zero line (positive) or to its left (negative), regardless of the value of their imaginary co-ordinate.

Same argument could be used for Im(z) too. Why is useful to define a sign of z as the projection along the Re axis?

--
Tor <torust [at] online [dot] no>
.

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