Given i^(2/7), I get the following result:
Which doesn’t look correct to me.
So, I entered “7th root of -1”, which gave me this:
Which is what I expected.
So I thought, perhaps these aren’t equivalent and I’ve gone wrong somewhere?
I entered “(7th root of -1) = i^(2/7)”:
WolframAlpha appears to be contradicting itself!
Looking more closely, the two seem to be rotations of one another.
Is this a bug, or am I missing something here?
Links
Noting that E^(I Pi(1+2n))=-1 for {n,0,6}
Do[Print[Re[E^(I Pi (1 + 2 n)/7)], " ",
Im[E^(I Pi (1 + 2 n)/7)]], {n, 0, 6}]
Cos[\[Pi]/7] Sin[\[Pi]/7]
Sin[\[Pi]/14] Cos[\[Pi]/14]
-Sin[(3 \[Pi])/14] Cos[(3 \[Pi])/14]
-1 0
-Sin[(3 \[Pi])/14] -Cos[(3 \[Pi])/14]
Sin[\[Pi]/14] -Cos[\[Pi]/14]
Cos[\[Pi]/7] -Sin[\[Pi]/7]
i agree something is amiss. Reported it as needing investigation.
Is this some form of source code?
Apologies if I’m missing something obvious, I am not particularly knowledgeable in the world of maths (this came from me experimenting with fractional powers of complex numbers to learn about them more deeply).
Thank you for your help, it did strike me as odd and my more mathematically adept peers at work agreed. Hopefully this will lead to an improvement in WolframAlpha in some way or form!
Nevermind, found out how to run it.
Thank you for finding this. We’ve fixed this today, and it should make it to the live site in about a week.
Glad to help! If you’re able to tell me, what was causing the issue? Otherwise thank you for such a great tool.
The numerator in the fractional exponent was being overlooked, so you were seeing the root plot for i^(1/7) instead of i^(2/7).
Ah right, that explains it. Thanks again!