Can I say that $1^{\frac{1}{2}} = (e^{2i\pi})^{\frac{1}{2}} =e^{i\pi} = -1 $?

Question

Can I say that $1^{\frac{1}{2}} = (e^{2i\pi})^{\frac{1}{2}} =e^{i\pi} = -1 $ ?

the Answer is obviously no, but why not ?

Cf. this question; the general rule $(a^m)^n=a^{m×n}$ does not always work when $m$ and $n$ are not integers — J. W. Tanner, Apr 19 '20 at 16:06

score 1 · Answer 1 · answered Apr 19 '20 at 16:05

1

Actually, you can see it as the solution of a complex equation where the the complex number $z$ and $-z$ are both solutions.

answered Apr 19 '20 at 16:05

Reda

1 Answers1