Q8Discrete Mathematics Structure

A group is cyclic if there exists an element $g\in G$ such that every element of $G$ can be written as $g^n$ for some integer $n$. For $G=\{1,-1,i,-i\}$ under multiplication:

• $i^1=i$
• $i^2=-1$
• $i^3=-i$
• $i^4=1$
• Since $i$ generates all elements, $G$ is cyclic. Similarly, $(-i)$ is also a generator.
• Generators: $\{i,-i\}$.