### 2018 AIME Problem 6

Posted:

**Thu Jan 10, 2019 11:09 pm**Let $N$ be the number of complex numbers $z$ with the properties that $|z|=1$ and $z^{6!}-z^{5!}$ is a real number. Find the remainder when $N$ is divided by $1000$.

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Posted: **Thu Jan 10, 2019 11:09 pm**

Let $N$ be the number of complex numbers $z$ with the properties that $|z|=1$ and $z^{6!}-z^{5!}$ is a real number. Find the remainder when $N$ is divided by $1000$.