Hi, I have a doubt concerning the following simple problem. This is actually a textbook problem, so the answer is correct. I just want to understand(adsbygoogle = window.adsbygoogle || []).push({}); whythis is.

1^(1/6) = exp ((1/6)(2n*[tex]\pi[/tex]i)) = cos (n*[tex]\pi[/tex]/3) + i sin (n*[tex]\pi[/tex]/3)

where n = 0,1,2,3,...

Ok, it is comprehensible that for n=0 we get cos(0) = 1, which is equal to 1^(1/6) = 1

However, I can't grasp why with n=1, for example, cis (n[tex]\pi[/tex]/3) is still equal to 1. In that case we would have cos([tex]\pi[/tex]/3) + i sin([tex]\pi[/tex]/3). How canthatbe equal to 1?! It has an imaginary part! Not even the real parts are equal.

The pi's appear as exponentials for some reason. Anyway, you get what I'm saying.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Why is 1^(1/6) equal to cis(n*pi/3)?

**Physics Forums | Science Articles, Homework Help, Discussion**