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plotting x^(1/3)

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When I plot x^(1/3)

I only see the red graph instead of red+blue. Is this supposed to happen?

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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

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Have a nice day !.
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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.

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¡ Hi!, @Roelandus:

If you change, the scales, of values of X, you can see, in the Wolfram Alpha ...

Kind Regards !.
Have a nice day !.
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
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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, 0.5-sin(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 sub-domain.

Cyrille

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