The principal root is the single-valued choice of an nth root obtained from the principal complex argument.
If 
is a positive
integer and a nonzero complex number is written
 |
where 
and 
,
then its principal 
th
root is
 |
All the nth roots are obtained by multiplying this value by the 
th
roots of unity. The principal root of 0 is 0.
For a positive real number, the principal root agrees with the positive real root.
For a negative real number and odd 
, it need not agree with the real
root. For example, the principal cube root of 
is 
, while its real cube root
is 
. In the Wolfram
Language, Power[z,
1/n] returns the principal root, whereas Surd[x,
n] returns the real root of a real
number when that root exists.
