Editing Euler's formula (section)

==Other special cases==
The [[special case]]s that evaluate to units illustrate rotation around the complex unit circle:

{|class="wikitable" style="text-align:right;"
! {{math|''x''}} !! {{math|1=''e<sup>ix</sup>''}}
|-
| {{math|0 + 2''πn''}} || {{math|1}}
|-
| {{math|{{sfrac|''π''|2}} + 2''πn''}} || {{math|''i''}}
|-
| {{math|''π'' + 2''πn''}} || {{math|−1}}
|-
| {{math|{{sfrac|''3π''|2}} + 2''πn''}} || {{math|−''i''}}
|}

The special case at {{math|1=''x'' = ''τ''}} (where {{math|1=''τ'' = 2''π''}}, one [[Turn (angle)|turn]]) yields {{math|1=''e<sup>iτ</sup>'' = 1 + 0}}. This is also argued to link five fundamental constants with three basic arithmetic operations, but, unlike Euler's identity, without rearranging the [[addend]]s from the general case:
<math display="block">\begin{align}
e^{i\tau} &= \cos \tau + i \sin \tau \\
&= 1 + 0
\end{align}</math>
An interpretation of the simplified form {{math|1=''e<sup>iτ</sup>'' = 1}} is that rotating by a full turn is an [[identity function]].<ref name="Hartl_2019">{{cite web |title=The Tau Manifesto |author-first=Michael |author-last=Hartl |author-link=Michael Hartl |date=2019-03-14 |orig-date=2010-03-14 |url=http://tauday.com/tau-manifesto |access-date=2013-09-14 |url-status=live |archive-url=https://web.archive.org/web/20190628230418/https://tauday.com/tau-manifesto |archive-date=2019-06-28}}</ref>