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 plotting x^(1/3)
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Solved!
plotting x^(1/3)
12122016 08:49 AM
When I plot x^(1/3)
I only see the red graph instead of red+blue. Is this supposed to happen?
Solved! Go to Solution.
12122016 10:52 AM  edited 12122016 11:55 AM
Hi!, @Roelandus:
Welcome to HP Forum !.
Try, with ...
Blue = real number part
Red = Imaginary number part
In comparison with Wolfram Alpha ... http://www.wolframalpha.com/input/?i=cubic+root+of+x
Have a nice day !.
@Maké (Technical Advisor Premium  HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
12122016 12:07 PM  edited 12122016 12:09 PM
X^(1/3)=cubic root of x, right?
That means that the graphs are identical,
But when I do X^(1/3):
And when I do the cubic root of X:
As you can see, the graphs aren't identical at all. But it could be that I'm doing something wrong. I'm not a professor unlike you
At my school we haven't had the subject 'imaginary numbers' yet. My uncle told me about it once though.
Thanks for your time!
12122016 04:14 PM  edited 12122016 04:15 PM
¡ Hi!, @Roelandus:
If you change, the scales, of values of X, you can see, in the Wolfram Alpha ...
Have a nice day !.
@Maké (Technical Advisor Premium  HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
12132016 12:17 AM
Hello,
"X^(1/3)=cubic root of x, right?"
Unfortunately, no. This is only true for X>=0
For X<0, X^ (1/3) has multiple solutions (3 in fact), which are 0.5+sin(60)*i, 0.5sin(60)*i and 1 (2 complex numbers and one real).
Since, in the general case, a negative number power a non integer number does NOT have a real root, the calcualtor returns the first complex root (this is conventional in math as it makes the power function continuous, and threefore differenciable).
The NthRoot function is a different function (even if it is equivalent to ^(1/N) for X>=0), it is not equivalent to it for X<0.
One reason is that NthRoot knows N (and not 1/N) and can test if N is an integer and do specific calculations in this case. power can not tell if 0.333...33 is the result of 1/3 or a true 0.3333...333? ^ can not tell)
I hope that this helps. The more you learn in math, the more you learn that a lot of what you were told earlier was a 1/2 truth or an aproximation, or limited to a specific subdomain.
Cyrille
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