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Is this a bug? i^(2/7) yields different results to 7th root of -1

Posted 10 years ago
POSTED BY: Joshua Gerrard
9 Replies

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]
POSTED BY: S M Blinder

i agree something is amiss. Reported it as needing investigation.

POSTED BY: Daniel Lichtblau
Posted 10 years ago

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).

POSTED BY: Joshua Gerrard
Posted 10 years ago

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!

POSTED BY: Joshua Gerrard
Posted 10 years ago
POSTED BY: Joshua Gerrard
Posted 10 years ago
POSTED BY: Greg Hurst
Posted 10 years ago

Glad to help! If you're able to tell me, what was causing the issue? Otherwise thank you for such a great tool.

POSTED BY: Joshua Gerrard
Posted 10 years ago

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).

POSTED BY: Greg Hurst
Posted 10 years ago

Ah right, that explains it. Thanks again!

POSTED BY: Joshua Gerrard
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