The number of distinct $n$th roots of a non-zero complex number is:
A$1$, since each number has only one root in $\mathbb{C}$ chart
B$n$, equally spaced on a circle of radius $r^{1/n}$ at origin
C$2$, since complex roots always come in conjugate pairs
D$n^2$, since $n$ roots are repeated with multiplicity $n$ each
Answer & Solution
Correct answer: B. $n$, equally spaced on a circle of radius $r^{1/n}$ at origin
A non-zero complex number has exactly $n$ distinct $n$th roots, on a circle of radius $r^{1/n}$, separated by $2\pi/n$.
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