Hello everyone,
I have a question concerning real and complex results. Consider the following calculation:
\(\begin{eqnarray}
x^{11} &=& \frac{18}{11}
\end{eqnarray}\)
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 \(\begin{eqnarray}x \cong 1,0034 + 0,2946i\end{eqnarray}\).
When I disable compelx results the calculator shows me an error "Invalid Data". The same goes for (I think) any odd root for a negative number.
Can the DM42/Free42 give the real result for such a calculation anyhow?
Question about a result
Re: Question about a result
both result are correct: they are two of the 11 complex roots of the number 11√(18/11).
See here and try with the program of DaveGary (or try in DM 41X with Math 1 pack module)
The 6th is real, the other are complex, DM42 and Free42 show the first, the Dave's program all.
Salvo
See here and try with the program of DaveGary (or try in DM 41X with Math 1 pack module)
The 6th is real, the other are complex, DM42 and Free42 show the first, the Dave's program all.
Salvo
∫aL√0mic (IT9CLU) :: DM42 (SN: 00881), DM41X (SN 00523), DM16, HP Prime, 50g, 41CX, 42s, 71b, 15C, 12C, 35s, WP34s  Free42
Re: Question about a result
Thank you very much, I will look into that!
I have to say, I'm not very familiar with complex numbers in general..
I have to say, I'm not very familiar with complex numbers in general..
Re: Question about a result
no problem at all
enjoy with DM42!
Salvo
EDIT: a bit of theory of nth Root of a complex number is here
∫aL√0mic (IT9CLU) :: DM42 (SN: 00881), DM41X (SN 00523), DM16, HP Prime, 50g, 41CX, 42s, 71b, 15C, 12C, 35s, WP34s  Free42
Re: Question about a result
I think it strange that HP calculators and derivates are not able to find the real solution 1.0458. I tried with HP 41, DM 15, DM 41X and HP prime. They all deliver an error message. If I try it with HP prime in CAS mode it delivers the imaginary solution 1.0034 + 0.2946i.
On the other side TI 89 Titanium and TI Nspire CX CAS deliver the right real result 1.0458.
Does anybody know why there is this difference?
On the other side TI 89 Titanium and TI Nspire CX CAS deliver the right real result 1.0458.
Does anybody know why there is this difference?
Re: Question about a result
18 [+/] [ENTER] 11 [/] 11 [xth_root_y] returns 1.045787917714882796046987298089874 on the WP43S. Just try it yourself.
For comparison: 18 [+/] [ENTER] 11 [/] 11 [1/x] [y^x] returns
1.003426158938366206140354971348624 + ix0.2946325039716886208438314513741246.
I guess that taking an odd (integer) root of negative number, the sign is separated, then the root is calculated of the absolute value, and the sign is added eventually.
(EDIT: corrected an error)
For comparison: 18 [+/] [ENTER] 11 [/] 11 [1/x] [y^x] returns
1.003426158938366206140354971348624 + ix0.2946325039716886208438314513741246.
I guess that taking an odd (integer) root of negative number, the sign is separated, then the root is calculated of the absolute value, and the sign is added eventually.
(EDIT: corrected an error)
DM42 SN: 00041 β
WP 43S running on this device
HP35, HP45, ..., HP35S, WP 34S, WP 31S, DM16L
WP 43S running on this device
HP35, HP45, ..., HP35S, WP 34S, WP 31S, DM16L

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Re: Question about a result
Since what you're calculating is not actually the 11th root but the 1/11th power, the results you are getting are correct.
If a calculator has an "xth root of y" button, it is not unreasonable to expect it to find the real 11th root of a negative number, but when calculating a power, the result is exp(x*ln(y)), and there is no ambiguity in what the result of that should be.
Re: Question about a result
The HP35s does (since it also has a [xth_root_y] key) ...I think it strange that HP calculators and derivates are not able to find the real solution 1.0458. I tried with HP 41, DM 15, DM 41X and HP prime.
18 [+/] [ENTER] 11 [/] 11 [xth_root_y] returns 1.04578791771 on the HP35s.
[35/45/65/67/25/29C/31E/33E/41CCVCX/71B/10C/11C/15C/16C/32SII/42S/28S/48GX/49G/35S/DM41X(#00456)]
(7397)[134]
(7397)[134]
Re: Question about a result
Even the HP6s (with [xth_root_y] key) returns 1.0457879178
Greetings,
Massimo
ajcaton
+×÷ left is right and right is wrong Casted in gold
Massimo
ajcaton
+×÷ left is right and right is wrong Casted in gold
Re: Question about a result
Thank you Walter, Thomas Okken, ecsfang and akaTB for your answers. Now it became clearer to me.
I tried as well with the TI calculators with using exact result and they deliver (11^(10/11)*3^(2/11)*2^(1/11))/11.
If you use the approx key they obviously calculate with CAS first this result which is approximated after that delivering 1.0458. The HPs (with the exception of the Prime) do not have CAS so they cannot use this.
I tried as well with the TI calculators with using exact result and they deliver (11^(10/11)*3^(2/11)*2^(1/11))/11.
If you use the approx key they obviously calculate with CAS first this result which is approximated after that delivering 1.0458. The HPs (with the exception of the Prime) do not have CAS so they cannot use this.