Prove that $\{x \in (\Bbb Z/p\Bbb Z)^\times : x^4 = 1\}$ is a cyclic subgroup of $(\Bbb Z/p\Bbb Z)^\times$ of order four.

Question

Let $p$ be a prime such that $4\mid p−1$. How do I prove that $\{x \in (\Bbb Z/p\Bbb Z)^\times : x^4 = 1\}$ is a cyclic subgroup of $(\Bbb Z/p\Bbb Z)^\times$ of order four?

I know that if $p$ is prime then $(\Bbb Z/p\Bbb Z)^\times$ is a cyclic group of order $p−1$ and I have also shown that $|g^k|=\frac{|g|}{\gcd(k,|g|)}$ but I am not sure where to go from here