Harald wrote:

Quote:

Well, there are three solutions to

-8 ENTER 3 XROOT

One of wich is -2,

...which is the only

*real* root. Since the 35s here is in real mode (all arguments are real), this is the only possible solution. So the returned result is fine.

Quote:

...and another one is 1 + 1,73205080757i

...which is exactly what the 35s returns in complex mode, i.e. when at least one of the arguments is complex. Just enter 8 as "8 i 0" and you'll get this result.

The third possible solution, i.e. the second complex one, is 1 - sqrt(3) i. But just as all other calculators I know of, the 35s returns just one possible solution:

In real mode that's either -2 (with 3 XROOT) or an error message (with 3 1/x y^{x}) since no real result exists.

In complex mode it's 1 + sqrt(3) i. It's the same as on any simple calculator with a [SQRT]-key which returns just one result, the positive root.

Quote:

...but couldn't

-8i0 ENTER 3 1/x y^{x}

also be -2 (+ 0.000000something*i to allow for the rounding error in 1/3)?

Hmmm... I am not an expert on complex arithmetics, but as far as I can see the real part of e.g. (-2 + 1E-15 i)

^{1/0.333333333333} will not equal 8 even when rounded to twelve digits, and the imaginary part will be small, but not zero.

But even if this *was* a possible solution: just as any other calculator, the 35s returns one single result. In this case the one that Wolfram Alpha returns as well. Which I think can be trusted. ;-)

Dieter

*Edited: 29 Sept 2013, 10:18 a.m. *