Question about a result

[Peet]

Interesting rounding results.

Walter said the WP43S returns -1.045787917714882796046987298089874

on the DM42:
18 [ENTER] 11 [/] 11 [1/x] [y^x] returns 1.045787917714882796046987298089873
18 [ENTER] 11 [/] [+/-] 11 [1/x] [y^x] [complex] [x^2] [x<>y] [x^2] [+] [SQRT] returns 1.045787917714882796046987298089872

[Over_score]

The correct answer is : https://www.wolframalpha.com/input/?i=- ... 82%2F11%29
-1.045787917714882796046987298089873586767669934361619669582805400....
So the correctly rounded result to 34 digits is -1.045787917714882796046987298089874
Thus, the WP43S shows THE correct result.

[Walter]

So the correctly rounded result to 34 digits is -1.045787917714882796046987298089874
Thus, the WP43S shows THE correct result.

What and who else?

[Peet]

Thus, the WP43S shows THE correct result.

or you can say the 42 truncates and the 43 rounds

[Stefan Karlsson]

To add to the list of HP calculators that have the \(\sqrt[x]{y}\) function and return the real result : HP 32SII.

The solver in DM42 will return the real result (but is of course more complicated to use).

Edit 1: Grammar.
Edit 2: The DM42 solver will find the real result.

[Jaymos]

What and who else?

\(\begin{eqnarray}
x^{11} &=& -\frac{18}{11}
\end{eqnarray}\)

Trying to calculate the result for x should give me the real number \(\begin{eqnarray}x \cong -1,046\end{eqnarray}\).
My DM42/Free42 gives me the complex result \(\begin{eqnarray}x \cong 1,0034 + 0,2946i\end{eqnarray}\).

Well, the other way is to look at the roots from the complex point of view, knowing that all roots are on the circle with the same radius as the real root, and knowing that one root will be negative, or at 180°.

if you do get a complex root using the way of powers as was discussed above,

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18 ENTER 11 / +/- 11 1/X Y^X

which renders 1.003...+ix0.295... then, since for the roots are all in polar form the same length at different angles, converting to polar,

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POLAR

renders 1.045...∠16.36...°, and

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COMPLEX X<>Y SHOW

also renders the size of all roots as 1.045787917714882796046987298089874 (WP43S / C43) with exactly the same rounding as before. I also fetched my WP34C from the drawer and confirm in double complex mode, the result is the same, ...874. Also checked WP34S on iPhone, also ...874. The DM42 and Free42 on my iPhone both render 1.045787917714882796046987298089872. (How I do like the DM42 skin of Free42 on the iPhone ... )