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Math Help - Number of solutions for z^n = a

  1. #1
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    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
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    [tex]n[\math]
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  3. #3
    MHF Contributor chiph588@'s Avatar
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    By the Fundamental Theorem of Algebra, a polynomial of degree  n will have  n roots in the complex numbers.
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  4. #4
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    z^n = c [/Math], with [Math]c \neq 0, has n roots (called the nth roots of unity). See Root of unity and Cyclotomic Polynomials on Wikipedia.
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