# Thread: Number of solutions for z^n = a

1. ## Number of solutions for z^n = a

Hello,
How many solutions are there for an equation of the form:
z^n = a
where z is (the unknown) complex, n is natural, a is real
if there's a more general answer for this, (for a real n, or a complex a, for example), it'll be nice to know also
thanks you

2. $$n[\math] 3. By the Fundamental Theorem of Algebra, a polynomial of degree $n$ will have $n$ roots in the complex numbers. 4. $z^n = c$$, with [tex]c \neq 0$, has $n$ roots (called the nth roots of unity). See Root of unity and Cyclotomic Polynomials on Wikipedia.